0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.14	% Command    : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.RFU7xDTJje
0.15/0.35	% Computer   : n027.cluster.edu
0.15/0.35	% Model      : x86_64 x86_64
0.15/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.15/0.35	% Memory     : 8042.1875MB
0.15/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.15/0.35	% CPULimit   : 1200
0.15/0.35	% DateTime   : Tue Jul 13 12:09:10 EDT 2021
0.15/0.35	% CPUTime    : 
0.15/0.35	% Running portfolio for 120 s
0.15/0.35	% File         : /export/starexec/sandbox/benchmark/theBenchmark.p
0.15/0.35	% Number of cores: 8
0.15/0.36	% Python version: Python 3.6.8
0.15/0.36	% Running in HO mode
0.56/0.64	% Estimated wc time : 1286
0.56/0.64	% Estimated cpu time (7 cpus) : 183.71428571428572
0.57/0.73	% /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s
0.57/0.73	% /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s
0.57/0.75	% /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s
0.57/0.76	% /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s
0.57/0.76	% /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s
0.58/0.76	% /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s
0.58/0.76	% /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s
29.10/4.86	% Solved by lams/old_b3.avatar.sh.
29.10/4.86	% done 2530 iterations in 4.030s
29.10/4.86	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
29.10/4.86	% SZS output start Refutation
29.10/4.86	tff(cTHM138, conjecture,
29.10/4.86	  (((((?[Xx]: cQ(Xx)) <=> (![Xy]: cR(Xy))) <=>
29.10/4.86	     (?[Xx]: (![Xy]: (cP(Xx) <=> cP(Xy))))) <=>
29.10/4.86	    ((?[Xx]: (![Xy]: (cQ(Xx) <=> cQ(Xy)))) <=>
29.10/4.86	     ((?[Xx]: cR(Xx)) <=> (![Xy]: cS(Xy))))) <=>
29.10/4.86	   (((?[Xx]: (![Xy]: (cS(Xx) <=> cS(Xy)))) <=>
29.10/4.86	     ((![Xy]: cQ(Xy)) <=> (?[Xx]: cP(Xx)))) <=>
29.10/4.86	    ((?[Xx]: (![Xy]: (cR(Xy) <=> cR(Xx)))) <=>
29.10/4.86	     ((![Xy]: cP(Xy)) <=> (?[Xx]: cS(Xx))))))).
29.10/4.86	tff(zf_stmt_0, negated_conjecture,
29.10/4.86	  (~
29.10/4.86	    (((((?[Xx]: cQ(Xx)) <=> (![Xy]: cR(Xy))) <=>
29.10/4.86	       (?[Xx]: (![Xy]: (cP(Xx) <=> cP(Xy))))) <=>
29.10/4.86	      ((?[Xx]: (![Xy]: (cQ(Xx) <=> cQ(Xy)))) <=>
29.10/4.86	       ((?[Xx]: cR(Xx)) <=> (![Xy]: cS(Xy))))) <=>
29.10/4.86	     (((?[Xx]: (![Xy]: (cS(Xx) <=> cS(Xy)))) <=>
29.10/4.86	       ((![Xy]: cQ(Xy)) <=> (?[Xx]: cP(Xx)))) <=>
29.10/4.86	      ((?[Xx]: (![Xy]: (cR(Xy) <=> cR(Xx)))) <=>
29.10/4.86	       ((![Xy]: cP(Xy)) <=> (?[Xx]: cS(Xx)))))))).
29.10/4.86	tff('0', plain,
29.10/4.86	    ((((??((^[Y0 : $i]: cQ(Y0)))) <=> (!!((^[Y0 : $i]: cR(Y0))))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	      ((??((^[Y0 : $i]: cR(Y0)))) <=> (!!((^[Y0 : $i]: cS(Y0)))))))
29.10/4.86	     != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	          ((!!((^[Y0 : $i]: cQ(Y0)))) <=> (??((^[Y0 : $i]: cP(Y0)))))) <=>
29.10/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!((^[Y0 : $i]: cP(Y0)))) <=> (??((^[Y0 : $i]: cS(Y0))))))),
29.10/4.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
29.10/4.86	tff('1', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	      ((??(cR)) <=> (!!(cS)))))
29.10/4.86	     != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	          ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('ho_norm', [status(thm)], ['0'])).
29.10/4.86	tff('2', plain,
29.10/4.86	    (~ ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	         ((??(cR)) <=> (!!(cS)))))
29.10/4.86	     | ~ (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	           ((!!(cP)) <=> (??(cS)))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['1'])).
29.10/4.86	tff('3', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	          ((??(cR)) <=> (!!(cS))))
29.10/4.86	     | ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	        ((!!(cQ)) <=> (??(cP))))
29.10/4.86	        != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	            ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['2'])).
29.10/4.86	tff('4', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	      ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!(cP)) <=> (??(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS)))))),
29.10/4.86	    inference('split', [status(esa)], ['3'])).
29.10/4.86	tff('5', plain,
29.10/4.86	    ((~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	         ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	           ((!!(cP)) <=> (??(cS))))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS)))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['4'])).
29.10/4.86	tff('6', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	       != ((!!(cQ)) <=> (??(cP)))
29.10/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	         != ((!!(cP)) <=> (??(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS)))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['5'])).
29.10/4.86	tff('7', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      != ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('split', [status(esa)], ['6'])).
29.10/4.86	tff('8', plain,
29.10/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      | ~ ((!!(cQ)) <=> (??(cP)))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['7'])).
29.10/4.86	tff('9', plain,
29.10/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      | (!!(cQ)) != (??(cP))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['8'])).
29.10/4.86	tff('10', plain, ((!!(cQ)) != (??(cP))) <= (~ ((!!(cQ)) = (??(cP)))),
29.10/4.86	    inference('split', [status(esa)], ['9'])).
29.10/4.86	tff('11', plain, (( (!!(cQ)) |  (??(cP)))) <= (~ ((!!(cQ)) = (??(cP)))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['10'])).
29.10/4.86	tff('12', plain, ((!!(cQ)) = (??(cP))) | ( (!!(cQ))) | ( (??(cP))),
29.10/4.86	    inference('split', [status(esa)], ['11'])).
29.10/4.86	tff('13', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	      ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!(cP)) <=> (??(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS)))))),
29.10/4.86	    inference('split', [status(esa)], ['3'])).
29.10/4.86	tff('14', plain,
29.10/4.86	    (( ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	        ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!(cP)) <=> (??(cS))))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS)))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['13'])).
29.10/4.86	tff('15', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	       = ((!!(cQ)) <=> (??(cP)))
29.10/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	         = ((!!(cP)) <=> (??(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS)))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['14'])).
29.10/4.86	tff('16', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      = ((!!(cP)) <=> (??(cS))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['15'])).
29.10/4.86	tff('17', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      != ((!!(cP)) <=> (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['6'])).
29.10/4.86	tff('18', plain,
29.10/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      | ~ ((!!(cP)) <=> (??(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['17'])).
29.10/4.86	tff('19', plain,
29.10/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      | (!!(cP)) != (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['18'])).
29.10/4.86	tff('20', plain,
29.10/4.86	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['19'])).
29.10/4.86	tff('21', plain,
29.10/4.86	    (~ ((!!(cP)) <=> (??(cS))))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('sup-', [status(thm)], ['16', '20'])).
29.10/4.86	tff('22', plain,
29.10/4.86	    ((!!(cP)) != (??(cS)))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['21'])).
29.10/4.86	tff('23', plain,
29.10/4.86	    (( (!!(cP)) |  (??(cS))))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['22'])).
29.10/4.86	tff('24', plain,
29.10/4.86	    ( (??(cS))) | 
29.10/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.10/4.86	    ( (!!(cP))) | 
29.10/4.86	    ~
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      = ((!!(cP)) <=> (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['23'])).
29.10/4.86	tff('25', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      != ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('split', [status(esa)], ['6'])).
29.10/4.86	tff('26', plain,
29.10/4.86	    (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      |  ((!!(cQ)) <=> (??(cP)))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['25'])).
29.10/4.86	tff('27', plain,
29.10/4.86	    (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      | (!!(cQ)) = (??(cP))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['26'])).
29.10/4.86	tff('28', plain,
29.10/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['27'])).
29.10/4.86	tff('29', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      != ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('split', [status(esa)], ['6'])).
29.10/4.86	tff('30', plain,
29.10/4.86	    (~ ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('sup-', [status(thm)], ['28', '29'])).
29.10/4.86	tff('31', plain,
29.10/4.86	    ((!!(cQ)) != (??(cP)))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['30'])).
29.10/4.86	tff('32', plain,
29.10/4.86	    (( (!!(cQ)) |  (??(cP))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['31'])).
29.10/4.86	tff('33', plain,
29.10/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.10/4.86	    ( (!!(cQ))) | ( (??(cP))) | 
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      = ((!!(cQ)) <=> (??(cP)))),
29.10/4.86	    inference('split', [status(esa)], ['32'])).
29.10/4.86	tff('34', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      = ((!!(cP)) <=> (??(cS))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['15'])).
29.10/4.86	tff('35', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      != ((!!(cP)) <=> (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['6'])).
29.10/4.86	tff('36', plain,
29.10/4.86	    (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      |  ((!!(cP)) <=> (??(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['35'])).
29.10/4.86	tff('37', plain,
29.10/4.86	    (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      | (!!(cP)) = (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['36'])).
29.10/4.86	tff('38', plain,
29.10/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['37'])).
29.10/4.86	tff('39', plain,
29.10/4.86	    ( ((!!(cP)) <=> (??(cS))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('sup+', [status(thm)], ['34', '38'])).
29.10/4.86	tff('40', plain,
29.10/4.86	    ((!!(cP)) = (??(cS)))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['39'])).
29.10/4.86	tff('41', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	      ((??(cR)) <=> (!!(cS)))))
29.10/4.86	     != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	          ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('ho_norm', [status(thm)], ['0'])).
29.10/4.86	tff('42', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	       ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	           ((!!(cP)) <=> (!!(cP))))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('sup-', [status(thm)], ['40', '41'])).
29.10/4.86	tff('43', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	       ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('simplify boolean subterms', [status(thm)], ['42'])).
29.10/4.86	tff('44', plain,
29.10/4.86	    ((~ ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	          ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      | ~ (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['43'])).
29.10/4.86	tff('45', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	           ((??(cR)) <=> (!!(cS))))
29.10/4.86	      | ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	         ((!!(cQ)) <=> (??(cP))))
29.10/4.86	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['44'])).
29.10/4.86	tff('46', plain,
29.10/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.10/4.86	    ~
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	      ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.10/4.86	    ~
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.10/4.86	    ~
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	         ((??(cR)) <=> (!!(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['45'])).
29.10/4.86	tff('47', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      = ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('split', [status(esa)], ['15'])).
29.10/4.86	tff('48', plain,
29.10/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['27'])).
29.10/4.86	tff('49', plain,
29.10/4.86	    ( ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('sup+', [status(thm)], ['47', '48'])).
29.10/4.86	tff('50', plain,
29.10/4.86	    ((!!(cQ)) = (??(cP)))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['49'])).
29.10/4.86	tff('51', plain,
29.10/4.86	    ((~ (!!(cQ)) |  (??(cP))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['50'])).
29.10/4.86	tff('52', plain,
29.10/4.86	    ~
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.10/4.86	    ~ ( (!!(cQ))) | ( (??(cP))) | 
29.10/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))),
29.10/4.86	    inference('split', [status(esa)], ['51'])).
29.10/4.86	tff('53', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      = ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('split', [status(esa)], ['15'])).
29.10/4.86	tff('54', plain,
29.10/4.86	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['9'])).
29.10/4.86	tff('55', plain,
29.10/4.86	    (~ ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('sup-', [status(thm)], ['53', '54'])).
29.10/4.86	tff('56', plain,
29.10/4.86	    ((!!(cQ)) != (??(cP)))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['55'])).
29.10/4.86	tff('57', plain,
29.10/4.86	    (( (!!(cQ)) |  (??(cP))))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['56'])).
29.10/4.86	tff('58', plain,
29.10/4.86	    ~
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.10/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.10/4.86	    ( (??(cP))) | ( (!!(cQ))), inference('split', [status(esa)], ['57'])).
29.10/4.86	tff('59', plain,
29.10/4.86	    ((!!(cP)) = (??(cS)))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['39'])).
29.10/4.86	tff('60', plain, ((!!(cP)) != (??(cS))) <= (~ ((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['19'])).
29.10/4.86	tff('61', plain, (( (!!(cP)) |  (??(cS)))) <= (~ ((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['60'])).
29.10/4.86	tff('62', plain, ( (??(cS))) <= (( (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['61'])).
29.10/4.86	tff('63', plain,
29.10/4.86	    ( (!!(cP)))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.10/4.86	          ( (??(cS)))),
29.10/4.86	    inference('sup+', [status(thm)], ['59', '62'])).
29.10/4.86	tff('64', plain, ((!!(cP)) = (??(cS))) <= (((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['37'])).
29.10/4.86	tff('65', plain, ( (??(cS))) <= (( (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['61'])).
29.10/4.86	tff('66', plain, ( (!!(cP))) <= (((!!(cP)) = (??(cS))) & ( (??(cS)))),
29.10/4.86	    inference('sup+', [status(thm)], ['64', '65'])).
29.10/4.86	tff('67', plain, (~ '#form3' |  (!!(cP))), define([status(thm)])).
29.10/4.86	tff('68', plain,
29.10/4.86	    ( '#form3')
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.10/4.86	          ( (??(cS)))),
29.10/4.86	    inference('renaming', [status(thm)], ['63', '67'])).
29.10/4.86	tff('69', plain, (~ '#form3' |  (!!(cP))), define([status(thm)])).
29.10/4.86	tff('70', plain, (~ '#form3') <= (~ ( '#form3')),
29.10/4.86	    inference('split', [status(esa)], ['69'])).
29.10/4.86	tff('71', plain,
29.10/4.86	    ~
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.10/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.10/4.86	    ( '#form3') | ~ ( (??(cS))),
29.10/4.86	    inference('sup-', [status(thm)], ['68', '70'])).
29.10/4.86	tff('72', plain, ((!!(cQ)) = (??(cP))) <= (((!!(cQ)) = (??(cP)))),
29.10/4.86	    inference('split', [status(esa)], ['27'])).
29.10/4.86	tff('73', plain, ((~ (!!(cQ)) |  (??(cP)))) <= (((!!(cQ)) = (??(cP)))),
29.10/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['72'])).
29.10/4.86	tff('74', plain, ~ ( (!!(cQ))) | ~ ((!!(cQ)) = (??(cP))) | ( (??(cP))),
29.10/4.86	    inference('split', [status(esa)], ['73'])).
29.10/4.86	tff('75', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	          ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.10/4.86	    inference('split', [status(esa)], ['3'])).
29.10/4.86	tff('76', plain,
29.10/4.86	    ((~ (((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	           ((??(cR)) <=> (!!(cS))))))
29.10/4.86	      <= (~
29.10/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['75'])).
29.10/4.86	tff('77', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR)))
29.10/4.86	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))
29.10/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	         != ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['76'])).
29.10/4.86	tff('78', plain,
29.10/4.86	    (((??(cQ)) <=> (!!(cR)))
29.10/4.86	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      <= (~
29.10/4.86	          (((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['77'])).
29.10/4.86	tff('79', plain,
29.10/4.86	    ((~ ((??(cQ)) <=> (!!(cR)))
29.10/4.86	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))))
29.10/4.86	      <= (~
29.10/4.86	          (((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['78'])).
29.10/4.86	tff('80', plain,
29.10/4.86	    (((??(cQ)) != (!!(cR))
29.10/4.86	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))))
29.10/4.86	      <= (~
29.10/4.86	          (((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['79'])).
29.10/4.86	tff('81', plain, ((??(cQ)) != (!!(cR))) <= (~ ((??(cQ)) = (!!(cR)))),
29.10/4.86	    inference('split', [status(esa)], ['80'])).
29.10/4.86	tff('82', plain, ((~ (??(cQ)) | ~ (!!(cR)))) <= (~ ((??(cQ)) = (!!(cR)))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['81'])).
29.10/4.86	tff('83', plain, ~ ( (??(cQ))) | ((??(cQ)) = (!!(cR))) | ~ ( (!!(cR))),
29.10/4.86	    inference('split', [status(esa)], ['82'])).
29.10/4.86	tff('84', plain,
29.10/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['37'])).
29.10/4.86	tff('85', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      != ((!!(cP)) <=> (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['6'])).
29.10/4.86	tff('86', plain,
29.10/4.86	    (~ ((!!(cP)) <=> (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('sup-', [status(thm)], ['84', '85'])).
29.10/4.86	tff('87', plain,
29.10/4.86	    ((!!(cP)) != (??(cS)))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['86'])).
29.10/4.86	tff('88', plain,
29.10/4.86	    (( (!!(cP)) |  (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['87'])).
29.10/4.86	tff('89', plain,
29.10/4.86	    ( (??(cS))) | 
29.10/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.10/4.86	    ( (!!(cP))) | 
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      = ((!!(cP)) <=> (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['88'])).
29.10/4.86	tff('90', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	      != ((??(cR)) <=> (!!(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['77'])).
29.10/4.86	tff('91', plain,
29.10/4.86	    (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	      |  ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['90'])).
29.10/4.86	tff('92', plain,
29.10/4.86	    (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	      | (??(cR)) = (!!(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['91'])).
29.10/4.86	tff('93', plain,
29.10/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['92'])).
29.10/4.86	tff('94', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	      != ((??(cR)) <=> (!!(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['77'])).
29.10/4.86	tff('95', plain,
29.10/4.86	    (~ ((??(cR)) <=> (!!(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.10/4.86	    inference('sup-', [status(thm)], ['93', '94'])).
29.10/4.86	tff('96', plain,
29.10/4.86	    ((??(cR)) != (!!(cS)))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['95'])).
29.10/4.86	tff('97', plain,
29.10/4.86	    ((~ (??(cR)) | ~ (!!(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['96'])).
29.10/4.86	tff('98', plain,
29.10/4.86	    ~ ( (!!(cS))) | ~ ( (??(cR))) | 
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.10/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
29.10/4.86	    inference('split', [status(esa)], ['97'])).
29.10/4.86	tff('99', plain,
29.10/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['27'])).
29.10/4.86	tff('100', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      = ((!!(cP)) <=> (??(cS))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['15'])).
29.10/4.86	tff('101', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	      ((??(cR)) <=> (!!(cS)))))
29.10/4.86	     != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	          ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('ho_norm', [status(thm)], ['0'])).
29.10/4.86	tff('102', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	       ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	          (((!!(cP)) <=> (??(cS))) <=> ((!!(cP)) <=> (??(cS))))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('sup-', [status(thm)], ['100', '101'])).
29.10/4.86	tff('103', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	       ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	          ((!!(cQ)) <=> (??(cP)))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('simplify boolean subterms', [status(thm)], ['102'])).
29.10/4.86	tff('104', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	       ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      != ($true <=> ((!!(cQ)) <=> (??(cP)))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('sup-', [status(thm)], ['99', '103'])).
29.10/4.86	tff('105', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	       ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      != ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('simplify boolean subterms', [status(thm)], ['104'])).
29.10/4.86	tff('106', plain,
29.10/4.86	    ((~ ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	          ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      | ~ ((!!(cQ)) <=> (??(cP)))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['105'])).
29.10/4.86	tff('107', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	           ((??(cR)) <=> (!!(cS))))
29.10/4.86	      | (!!(cQ)) != (??(cP))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['106'])).
29.10/4.86	tff('108', plain,
29.10/4.86	    ~
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.10/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.10/4.86	    ~ ((!!(cQ)) = (??(cP))) | 
29.10/4.86	    ~
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      = ((!!(cP)) <=> (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['107'])).
29.10/4.86	tff('109', plain, ((!!(cP)) = (??(cS))) <= (((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['37'])).
29.10/4.86	tff('110', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	      ((??(cR)) <=> (!!(cS)))))
29.10/4.86	     != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	          ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('ho_norm', [status(thm)], ['0'])).
29.10/4.86	tff('111', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	       ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	           ((!!(cP)) <=> (!!(cP))))))
29.10/4.86	      <= (((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('sup-', [status(thm)], ['109', '110'])).
29.10/4.86	tff('112', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	       ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.10/4.86	      <= (((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('simplify boolean subterms', [status(thm)], ['111'])).
29.10/4.86	tff('113', plain,
29.10/4.86	    (( ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	         ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      |  (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))))
29.10/4.86	      <= (((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['112'])).
29.10/4.86	tff('114', plain,
29.10/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	          ((??(cR)) <=> (!!(cS))))
29.10/4.86	      | ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	         ((!!(cQ)) <=> (??(cP))))
29.10/4.86	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.10/4.86	      <= (((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['113'])).
29.10/4.86	tff('115', plain,
29.10/4.86	    ~ ((!!(cP)) = (??(cS))) | 
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	      ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	         ((??(cR)) <=> (!!(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['114'])).
29.10/4.86	tff('116', plain, ((??(cR)) = (!!(cS))) <= (((??(cR)) = (!!(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['92'])).
29.10/4.86	tff('117', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	      != ((??(cR)) <=> (!!(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['77'])).
29.10/4.86	tff('118', plain,
29.10/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	      | ~ ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['117'])).
29.10/4.86	tff('119', plain,
29.10/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	      | (??(cR)) != (!!(cS))))
29.10/4.86	      <= (~
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['118'])).
29.10/4.86	tff('120', plain, ((??(cR)) != (!!(cS))) <= (~ ((??(cR)) = (!!(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['119'])).
29.10/4.86	tff('121', plain, (( (??(cR)) |  (!!(cS)))) <= (~ ((??(cR)) = (!!(cS)))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['120'])).
29.10/4.86	tff('122', plain, ( (??(cR))) <= (( (??(cR)))),
29.10/4.86	    inference('split', [status(esa)], ['121'])).
29.10/4.86	tff('123', plain, ( (!!(cS))) <= (((??(cR)) = (!!(cS))) & ( (??(cR)))),
29.10/4.86	    inference('sup+', [status(thm)], ['116', '122'])).
29.10/4.86	tff('124', plain, ( (!!(cS))) <= (((??(cR)) = (!!(cS))) & ( (??(cR)))),
29.10/4.86	    inference('sup+', [status(thm)], ['116', '122'])).
29.10/4.86	tff('125', plain, (~ '#form14' |  (!!(cS))), define([status(thm)])).
29.10/4.86	tff('126', plain, ( '#form14') <= (((??(cR)) = (!!(cS))) & ( (??(cR)))),
29.10/4.86	    inference('renaming', [status(thm)], ['123', '125'])).
29.10/4.86	tff('127', plain, (~ '#form14' |  (!!(cS))), define([status(thm)])).
29.10/4.86	tff('128', plain, (~ '#form14') <= (~ ( '#form14')),
29.10/4.86	    inference('split', [status(esa)], ['127'])).
29.10/4.86	tff('129', plain, ~ ((??(cR)) = (!!(cS))) | ( '#form14') | ~ ( (??(cR))),
29.10/4.86	    inference('sup-', [status(thm)], ['126', '128'])).
29.10/4.86	tff('130', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	      ((??(cR)) <=> (!!(cS)))))
29.10/4.86	     != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	          ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('ho_norm', [status(thm)], ['0'])).
29.10/4.86	tff('131', plain,
29.10/4.86	    ( ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.10/4.86	       ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	        ((??(cR)) <=> (!!(cS)))))
29.10/4.86	     |  (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	          ((!!(cQ)) <=> (??(cP)))) <=>
29.10/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!(cP)) <=> (??(cS)))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['130'])).
29.10/4.86	tff('132', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	         ((??(cR)) <=> (!!(cS))))
29.10/4.86	     | ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	        ((!!(cQ)) <=> (??(cP))))
29.10/4.86	        = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	           ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['131'])).
29.10/4.86	tff('133', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	         ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.10/4.86	    inference('split', [status(esa)], ['132'])).
29.10/4.86	tff('134', plain,
29.10/4.86	    ((~ (((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	          ((??(cR)) <=> (!!(cS))))))
29.10/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.10/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['133'])).
29.10/4.86	tff('135', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR)))
29.10/4.86	       != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))
29.10/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	         = ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['134'])).
29.10/4.86	tff('136', plain,
29.10/4.86	    ~
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.10/4.86	    ~
29.10/4.86	    (((??(cQ)) <=> (!!(cR)))
29.10/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	      = ((??(cR)) <=> (!!(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['135'])).
29.10/4.86	tff('137', plain,
29.10/4.86	    (((??(cQ)) <=> (!!(cR)))
29.10/4.86	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      <= (~
29.10/4.86	          (((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['77'])).
29.10/4.86	tff('138', plain,
29.10/4.86	    (( ((??(cQ)) <=> (!!(cR)))
29.10/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))))
29.10/4.86	      <= (~
29.10/4.86	          (((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['137'])).
29.10/4.86	tff('139', plain,
29.10/4.86	    (((??(cQ)) = (!!(cR))
29.10/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))))
29.10/4.86	      <= (~
29.10/4.86	          (((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['138'])).
29.10/4.86	tff('140', plain, ((??(cQ)) = (!!(cR))) <= (((??(cQ)) = (!!(cR)))),
29.10/4.86	    inference('split', [status(esa)], ['139'])).
29.10/4.86	tff('141', plain, (~ (!!(cR))) <= (~ ( (!!(cR)))),
29.10/4.86	    inference('split', [status(esa)], ['82'])).
29.10/4.86	tff('142', plain, (~ (??(cQ))) <= (~ ( (!!(cR))) & ((??(cQ)) = (!!(cR)))),
29.10/4.86	    inference('sup-', [status(thm)], ['140', '141'])).
29.10/4.86	tff('143', plain, ( '#form13' | ~ (??(cQ))), define([status(thm)])).
29.10/4.86	tff('144', plain, ( '#form13') <= (( '#form13')),
29.10/4.86	    inference('split', [status(esa)], ['143'])).
29.10/4.86	tff('145', plain, ((??(cQ)) != (!!(cR))) <= (~ ((??(cQ)) = (!!(cR)))),
29.10/4.86	    inference('split', [status(esa)], ['80'])).
29.10/4.86	tff('146', plain, (( (??(cQ)) |  (!!(cR)))) <= (~ ((??(cQ)) = (!!(cR)))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['145'])).
29.10/4.86	tff('147', plain, ( (!!(cR))) <= (( (!!(cR)))),
29.10/4.86	    inference('split', [status(esa)], ['146'])).
29.10/4.86	tff('148', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	          ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.10/4.86	    inference('split', [status(esa)], ['3'])).
29.10/4.86	tff('149', plain,
29.10/4.86	    (( (((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	          ((??(cR)) <=> (!!(cS))))))
29.10/4.86	      <= (~
29.10/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['148'])).
29.10/4.86	tff('150', plain,
29.10/4.86	    ((((??(cQ)) <=> (!!(cR)))
29.10/4.86	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))
29.10/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.10/4.86	         = ((??(cR)) <=> (!!(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.10/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.10/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['149'])).
29.10/4.86	tff('151', plain,
29.10/4.86	    (((??(cQ)) <=> (!!(cR)))
29.10/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['150'])).
29.10/4.86	tff('152', plain,
29.10/4.86	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['80'])).
29.10/4.86	tff('153', plain,
29.10/4.86	    (~ ((??(cQ)) <=> (!!(cR))))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.10/4.86	          (((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.10/4.86	    inference('sup-', [status(thm)], ['151', '152'])).
29.10/4.86	tff('154', plain,
29.10/4.86	    ((??(cQ)) != (!!(cR)))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.10/4.86	          (((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['153'])).
29.10/4.86	tff('155', plain,
29.10/4.86	    (~ (??(cQ)))
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.10/4.86	          (((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.10/4.86	          ( (!!(cR)))),
29.10/4.86	    inference('sup-', [status(thm)], ['147', '154'])).
29.10/4.86	tff('156', plain, ( '#form13' | ~ (??(cQ))), define([status(thm)])).
29.10/4.86	tff('157', plain,
29.10/4.86	    (~ '#form13')
29.10/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.10/4.86	          (((??(cQ)) <=> (!!(cR)))
29.10/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.10/4.86	          ( (!!(cR)))),
29.10/4.86	    inference('renaming', [status(thm)], ['155', '156'])).
29.10/4.86	tff('158', plain,
29.10/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.10/4.86	    ~
29.10/4.86	    (((??(cQ)) <=> (!!(cR)))
29.10/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.10/4.86	    ~ ( (!!(cR))) | ~ ( '#form13'),
29.10/4.86	    inference('sup-', [status(thm)], ['144', '157'])).
29.10/4.86	tff('159', plain,
29.10/4.86	    ((!!(cP)) = (??(cS)))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['39'])).
29.10/4.86	tff('160', plain, ( (??(cS))) <= (( (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['61'])).
29.10/4.86	tff('161', plain,
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      = ((!!(cP)) <=> (??(cS))))
29.10/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.10/4.86	    inference('split', [status(esa)], ['15'])).
29.10/4.86	tff('162', plain, ( (!!(cP))) <= (( (!!(cP)))),
29.10/4.86	    inference('split', [status(esa)], ['61'])).
29.10/4.86	tff('163', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	      ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ((!!(cP)) <=> (??(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS)))))),
29.10/4.86	    inference('split', [status(esa)], ['3'])).
29.10/4.86	tff('164', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	      ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          ($true <=> (??(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.10/4.86	          ( (!!(cP)))),
29.10/4.86	    inference('sup-', [status(thm)], ['162', '163'])).
29.10/4.86	tff('165', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	      ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	          (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.10/4.86	          ( (!!(cP)))),
29.10/4.86	    inference('simplify boolean subterms', [status(thm)], ['164'])).
29.10/4.86	tff('166', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	      ((!!(cQ)) <=> (??(cP)))) != (((!!(cP)) <=> (??(cS))) <=> (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (!!(cP)))),
29.10/4.86	    inference('sup-', [status(thm)], ['161', '165'])).
29.10/4.86	tff('167', plain,
29.10/4.86	    ((~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	         ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      | ~ (((!!(cP)) <=> (??(cS))) <=> (??(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (!!(cP)))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['166'])).
29.10/4.86	tff('168', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	       != ((!!(cQ)) <=> (??(cP)))
29.10/4.86	      | ((!!(cP)) <=> (??(cS))) != (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (!!(cP)))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['167'])).
29.10/4.86	tff('169', plain,
29.10/4.86	    (((!!(cP)) <=> (??(cS))) != (??(cS)))
29.10/4.86	      <= (~ (((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['168'])).
29.10/4.86	tff('170', plain,
29.10/4.86	    (((!!(cP)) <=> $true) != (??(cS)))
29.10/4.86	      <= (~ (((!!(cP)) <=> (??(cS))) = (??(cS))) & ( (??(cS)))),
29.10/4.86	    inference('sup-', [status(thm)], ['160', '169'])).
29.10/4.86	tff('171', plain,
29.10/4.86	    ((!!(cP)) != (??(cS)))
29.10/4.86	      <= (~ (((!!(cP)) <=> (??(cS))) = (??(cS))) & ( (??(cS)))),
29.10/4.86	    inference('simplify boolean subterms', [status(thm)], ['170'])).
29.10/4.86	tff('172', plain,
29.10/4.86	    ((!!(cP)) != (!!(cP)))
29.10/4.86	      <= (~ (((!!(cP)) <=> (??(cS))) = (??(cS))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.10/4.86	          ( (??(cS)))),
29.10/4.86	    inference('sup-', [status(thm)], ['159', '171'])).
29.10/4.86	tff('173', plain,
29.10/4.86	    ~
29.10/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.10/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.10/4.86	    ~ ( (??(cS))) | (((!!(cP)) <=> (??(cS))) = (??(cS))),
29.10/4.86	    inference('simplify', [status(thm)], ['172'])).
29.10/4.86	tff('174', plain, ( (??(cS))) <= (( (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['61'])).
29.10/4.86	tff('175', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	      ((!!(cQ)) <=> (??(cP)))) != (((!!(cP)) <=> (??(cS))) <=> (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (!!(cP)))),
29.10/4.86	    inference('sup-', [status(thm)], ['161', '165'])).
29.10/4.86	tff('176', plain,
29.10/4.86	    (( ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	        ((!!(cQ)) <=> (??(cP))))
29.10/4.86	      |  (((!!(cP)) <=> (??(cS))) <=> (??(cS)))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (!!(cP)))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['175'])).
29.10/4.86	tff('177', plain,
29.10/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.10/4.86	       = ((!!(cQ)) <=> (??(cP)))
29.10/4.86	      | ((!!(cP)) <=> (??(cS))) = (??(cS))))
29.10/4.86	      <= (~
29.10/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.10/4.86	            ((!!(cQ)) <=> (??(cP))))
29.10/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.10/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.10/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.10/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.10/4.86	          ( (!!(cP)))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['176'])).
29.10/4.86	tff('178', plain,
29.10/4.86	    (((!!(cP)) <=> (??(cS))) = (??(cS)))
29.10/4.86	      <= ((((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['177'])).
29.10/4.86	tff('179', plain,
29.10/4.86	    (((!!(cP)) <=> $true) = (??(cS)))
29.10/4.86	      <= (( (??(cS))) & (((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.10/4.86	    inference('sup+', [status(thm)], ['174', '178'])).
29.10/4.86	tff('180', plain,
29.10/4.86	    ((!!(cP)) = (??(cS)))
29.10/4.86	      <= (( (??(cS))) & (((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.10/4.86	    inference('simplify boolean subterms', [status(thm)], ['179'])).
29.10/4.86	tff('181', plain, ( (??(cS))) <= (( (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['61'])).
29.10/4.86	tff('182', plain,
29.10/4.86	    ( (!!(cP))) <= (( (??(cS))) & (((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.10/4.86	    inference('sup+', [status(thm)], ['180', '181'])).
29.10/4.86	tff('183', plain, (~ '#form3' |  (!!(cP))), define([status(thm)])).
29.10/4.86	tff('184', plain,
29.10/4.86	    ( '#form3') <= (( (??(cS))) & (((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.10/4.86	    inference('renaming', [status(thm)], ['182', '183'])).
29.10/4.86	tff('185', plain, (~ '#form3') <= (~ ( '#form3')),
29.10/4.86	    inference('split', [status(esa)], ['69'])).
29.10/4.86	tff('186', plain,
29.10/4.86	    ~ (((!!(cP)) <=> (??(cS))) = (??(cS))) | ~ ( (??(cS))) | ( '#form3'),
29.10/4.86	    inference('sup-', [status(thm)], ['184', '185'])).
29.10/4.86	tff('187', plain, ( (!!(cP))) <= (((!!(cP)) = (??(cS))) & ( (??(cS)))),
29.10/4.86	    inference('sup+', [status(thm)], ['64', '65'])).
29.10/4.86	tff('188', plain, (~ '#form3' |  (!!(cP))), define([status(thm)])).
29.10/4.86	tff('189', plain, ( '#form3') <= (((!!(cP)) = (??(cS))) & ( (??(cS)))),
29.10/4.86	    inference('renaming', [status(thm)], ['187', '188'])).
29.10/4.86	tff('190', plain, (~ '#form3') <= (~ ( '#form3')),
29.10/4.86	    inference('split', [status(esa)], ['69'])).
29.10/4.86	tff('191', plain, ~ ((!!(cP)) = (??(cS))) | ~ ( (??(cS))) | ( '#form3'),
29.10/4.86	    inference('sup-', [status(thm)], ['189', '190'])).
29.10/4.86	tff('192', plain, ((!!(cP)) = (??(cS))) <= (((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['37'])).
29.10/4.86	tff('193', plain, ((!!(cP)) != (??(cS))) <= (~ ((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['19'])).
29.10/4.86	tff('194', plain, ((~ (!!(cP)) | ~ (??(cS)))) <= (~ ((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('lazy_cnf_xor', [status(thm)], ['193'])).
29.10/4.86	tff('195', plain, (~ (??(cS))) <= (~ ( (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['194'])).
29.10/4.86	tff('196', plain, (~ (!!(cP))) <= (~ ( (??(cS))) & ((!!(cP)) = (??(cS)))),
29.10/4.86	    inference('sup-', [status(thm)], ['192', '195'])).
29.10/4.86	tff('197', plain, ( '#form3' | ~ (!!(cP))), define([status(thm)])).
29.10/4.86	tff('198', plain, ( '#form3') <= (( '#form3')),
29.10/4.86	    inference('split', [status(esa)], ['197'])).
29.10/4.86	tff('199', plain, (~ (!!(cP))) <= (~ ( (!!(cP)))),
29.10/4.86	    inference('split', [status(esa)], ['197'])).
29.10/4.86	tff('200', plain, ( '#form3' | ~ (!!(cP))), define([status(thm)])).
29.10/4.86	tff('201', plain, (~ '#form3') <= (~ ( (!!(cP)))),
29.10/4.86	    inference('renaming', [status(thm)], ['199', '200'])).
29.10/4.86	tff('202', plain, ~ ( '#form3') | ( (!!(cP))),
29.10/4.86	    inference('sup-', [status(thm)], ['198', '201'])).
29.10/4.86	tff('203', plain,
29.10/4.86	    (((!!(cP)) <=> (??(cS))) = (??(cS)))
29.10/4.86	      <= ((((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['177'])).
29.10/4.86	tff('204', plain,
29.10/4.86	    ((~ ((!!(cP)) <=> (??(cS))) |  (??(cS))))
29.10/4.86	      <= ((((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.10/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['203'])).
29.10/4.86	tff('205', plain,
29.10/4.86	    (((!!(cP)) != (??(cS)) |  (??(cS))))
29.10/4.86	      <= ((((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['204'])).
29.10/4.86	tff('206', plain,
29.10/4.86	    ~ (((!!(cP)) <=> (??(cS))) = (??(cS))) | ~ ((!!(cP)) = (??(cS))) | 
29.10/4.86	    ( (??(cS))), inference('split', [status(esa)], ['205'])).
29.10/4.86	tff('207', plain, ( (??(cS))) <= (( (??(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['61'])).
29.10/4.86	tff('208', plain, ( cS('#sk2')) <= (( (??(cS)))),
29.10/4.86	    inference('lazy_cnf_exists', [status(thm)], ['207'])).
29.10/4.86	tff('209', plain,
29.10/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('split', [status(esa)], ['27'])).
29.10/4.86	tff('210', plain,
29.10/4.86	    ( (!!((^[Y0 : $i]: (cS('#sk18') <=> cS(Y0))))))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('lazy_cnf_exists', [status(thm)], ['209'])).
29.10/4.86	tff('211', plain,
29.10/4.86	    (![X1]:  (cS('#sk18') <=> cS(X1)))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('lazy_cnf_forall', [status(thm)], ['210'])).
29.10/4.86	tff('212', plain,
29.10/4.86	    (![X1]: cS('#sk18') = cS(X1))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['211'])).
29.10/4.86	tff('213', plain,
29.10/4.86	    (![X1]: cS('#sk18') = cS(X1))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('simplify nested equalities', [status(thm)], ['211'])).
29.10/4.86	tff('214', plain,
29.10/4.86	    (![X0, X1]: cS(X0) = cS(X1))
29.10/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.10/4.86	    inference('sup+', [status(thm)], ['212', '213'])).
29.10/4.86	tff('215', plain, ( (??(cR))) <= (( (??(cR)))),
29.10/4.86	    inference('split', [status(esa)], ['121'])).
29.10/4.86	tff('216', plain, ((??(cR)) != (!!(cS))) <= (~ ((??(cR)) = (!!(cS)))),
29.10/4.86	    inference('split', [status(esa)], ['119'])).
29.10/4.86	tff('217', plain, (~ (!!(cS))) <= (~ ((??(cR)) = (!!(cS))) & ( (??(cR)))),
29.10/4.86	    inference('sup-', [status(thm)], ['215', '216'])).
29.10/4.86	tff('218', plain, (~ cS('#sk11')) <= (~ ((??(cR)) = (!!(cS))) & ( (??(cR)))),
29.10/4.86	    inference('lazy_cnf_exists', [status(thm)], ['217'])).
29.10/4.86	tff('219', plain,
29.10/4.86	    (![X0]: ~ cS(X0))
29.10/4.86	      <= (~ ((??(cR)) = (!!(cS))) & 
29.10/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.10/4.86	          ( (??(cR)))),
29.10/4.86	    inference('sup-', [status(thm)], ['214', '218'])).
29.10/4.86	tff('220', plain,
29.10/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.16/4.86	    ~ ( (??(cR))) | ~ ( (??(cS))) | ((??(cR)) = (!!(cS))),
29.16/4.86	    inference('sup-', [status(thm)], ['208', '219'])).
29.16/4.86	tff('221', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['114'])).
29.16/4.86	tff('222', plain,
29.16/4.86	    ((~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	         ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['221'])).
29.16/4.86	tff('223', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	       != ((!!(cQ)) <=> (??(cP)))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['222'])).
29.16/4.86	tff('224', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ~
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))),
29.16/4.86	    inference('split', [status(esa)], ['223'])).
29.16/4.86	tff('225', plain,
29.16/4.86	    ((??(cR)) != (!!(cS)))
29.16/4.86	      <= (~
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['95'])).
29.16/4.86	tff('226', plain,
29.16/4.86	    (( (??(cR)) |  (!!(cS))))
29.16/4.86	      <= (~
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['225'])).
29.16/4.86	tff('227', plain,
29.16/4.86	    ( (??(cR))) | ( (!!(cS))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['226'])).
29.16/4.86	tff('228', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['37'])).
29.16/4.86	tff('229', plain, ( (!!(cP))) <= (( (!!(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('230', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS)))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS)))))),
29.16/4.86	    inference('split', [status(esa)], ['132'])).
29.16/4.86	tff('231', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ($true <=> (??(cS)))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('sup+', [status(thm)], ['229', '230'])).
29.16/4.86	tff('232', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         (??(cS))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['231'])).
29.16/4.86	tff('233', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) = ($true <=> (??(cS))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('sup+', [status(thm)], ['228', '232'])).
29.16/4.86	tff('234', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) = (??(cS)))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['233'])).
29.16/4.86	tff('235', plain,
29.16/4.86	    ((~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	         ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      |  (??(cS))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['234'])).
29.16/4.86	tff('236', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	       != ((!!(cQ)) <=> (??(cP)))
29.16/4.86	      |  (??(cS))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['235'])).
29.16/4.86	tff('237', plain,
29.16/4.86	    ~ ( (!!(cP))) | 
29.16/4.86	    ~
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ( (??(cS))), inference('split', [status(esa)], ['236'])).
29.16/4.86	tff('238', plain, ((??(cR)) = (!!(cS))) <= (((??(cR)) = (!!(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['92'])).
29.16/4.86	tff('239', plain, ((~ (??(cR)) |  (!!(cS)))) <= (((??(cR)) = (!!(cS)))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['238'])).
29.16/4.86	tff('240', plain, ~ ((??(cR)) = (!!(cS))) | ~ ( (??(cR))) | ( (!!(cS))),
29.16/4.86	    inference('split', [status(esa)], ['239'])).
29.16/4.86	tff('241', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
29.16/4.86	    ((??(cR)) = (!!(cS))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['92'])).
29.16/4.86	tff('242', plain, ( (!!(cP))) <= (( (!!(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('243', plain, ( (??(cS))) <= (( (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('244', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	      ((??(cR)) <=> (!!(cS)))))
29.16/4.86	     != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	          ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('ho_norm', [status(thm)], ['0'])).
29.16/4.86	tff('245', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	           ((!!(cP)) <=> $true))))
29.16/4.86	      <= (( (??(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['243', '244'])).
29.16/4.86	tff('246', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	           (!!(cP)))))
29.16/4.86	      <= (( (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['245'])).
29.16/4.86	tff('247', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	           $true)))
29.16/4.86	      <= (( (??(cS))) & ( (!!(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['242', '246'])).
29.16/4.86	tff('248', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (( (??(cS))) & ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['247'])).
29.16/4.86	tff('249', plain,
29.16/4.86	    ((~ ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      | ~ (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))))
29.16/4.86	      <= (( (??(cS))) & ( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['248'])).
29.16/4.86	tff('250', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	           ((??(cR)) <=> (!!(cS))))
29.16/4.86	      | ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	         ((!!(cQ)) <=> (??(cP))))
29.16/4.86	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (( (??(cS))) & ( (!!(cP)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['249'])).
29.16/4.86	tff('251', plain,
29.16/4.86	    ~ ( (!!(cP))) | ~ ( (??(cS))) | 
29.16/4.86	    ~
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.16/4.86	    ~
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))),
29.16/4.86	    inference('split', [status(esa)], ['250'])).
29.16/4.86	tff('252', plain,
29.16/4.86	    ( '#form3') <= (( (??(cS))) & (((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.16/4.86	    inference('renaming', [status(thm)], ['182', '183'])).
29.16/4.86	tff('253', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('split', [status(esa)], ['15'])).
29.16/4.86	tff('254', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['37'])).
29.16/4.86	tff('255', plain, ( (??(cS))) <= (( (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('256', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          ((!!(cP)) <=> (??(cS)))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS)))))),
29.16/4.86	    inference('split', [status(esa)], ['3'])).
29.16/4.86	tff('257', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          ((!!(cP)) <=> $true)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['255', '256'])).
29.16/4.86	tff('258', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['257'])).
29.16/4.86	tff('259', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) != ($true <=> (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['254', '258'])).
29.16/4.86	tff('260', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) != (!!(cP)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['259'])).
29.16/4.86	tff('261', plain,
29.16/4.86	    ((((!!(cQ)) <=> (??(cP))) <=> ((!!(cQ)) <=> (??(cP)))) != (!!(cP)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['253', '260'])).
29.16/4.86	tff('262', plain,
29.16/4.86	    (~ (!!(cP)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['261'])).
29.16/4.86	tff('263', plain, ( '#form3' | ~ (!!(cP))), define([status(thm)])).
29.16/4.86	tff('264', plain,
29.16/4.86	    (~ '#form3')
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('renaming', [status(thm)], ['262', '263'])).
29.16/4.86	tff('265', plain,
29.16/4.86	    ~ (((!!(cP)) <=> (??(cS))) = (??(cS))) | ~ ( (??(cS))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('sup-', [status(thm)], ['252', '264'])).
29.16/4.86	tff('266', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['111'])).
29.16/4.86	tff('267', plain,
29.16/4.86	    ((~ ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      | ~ (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	           (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))))
29.16/4.86	      <= (((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['266'])).
29.16/4.86	tff('268', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	           ((??(cR)) <=> (!!(cS))))
29.16/4.86	      | ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	         ((!!(cQ)) <=> (??(cP))))
29.16/4.86	         != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['267'])).
29.16/4.86	tff('269', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['268'])).
29.16/4.86	tff('270', plain,
29.16/4.86	    ((~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	         ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['269'])).
29.16/4.86	tff('271', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	       != ((!!(cQ)) <=> (??(cP)))
29.16/4.86	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['270'])).
29.16/4.86	tff('272', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))),
29.16/4.86	    inference('split', [status(esa)], ['271'])).
29.16/4.86	tff('273', plain, ( (!!(cP))) <= (( (!!(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('274', plain,
29.16/4.86	    (((!!(cP)) <=> (??(cS))) != (??(cS)))
29.16/4.86	      <= (~ (((!!(cP)) <=> (??(cS))) = (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['168'])).
29.16/4.86	tff('275', plain,
29.16/4.86	    (($true <=> (??(cS))) != (??(cS)))
29.16/4.86	      <= (~ (((!!(cP)) <=> (??(cS))) = (??(cS))) & ( (!!(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['273', '274'])).
29.16/4.86	tff('276', plain,
29.16/4.86	    ((??(cS)) != (??(cS)))
29.16/4.86	      <= (~ (((!!(cP)) <=> (??(cS))) = (??(cS))) & ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['275'])).
29.16/4.86	tff('277', plain, ~ ( (!!(cP))) | (((!!(cP)) <=> (??(cS))) = (??(cS))),
29.16/4.86	    inference('simplify', [status(thm)], ['276'])).
29.16/4.86	tff('278', plain,
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['150'])).
29.16/4.86	tff('279', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      <= (~
29.16/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.16/4.86	    inference('split', [status(esa)], ['3'])).
29.16/4.86	tff('280', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=> ((??(cQ)) <=> (!!(cR))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      <= (~
29.16/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['278', '279'])).
29.16/4.86	tff('281', plain,
29.16/4.86	    (~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	        ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      <= (~
29.16/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['280'])).
29.16/4.86	tff('282', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      != ((??(cR)) <=> (!!(cS))))
29.16/4.86	      <= (~
29.16/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['281'])).
29.16/4.86	tff('283', plain,
29.16/4.86	    ( '#form27'
29.16/4.86	     | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    define([status(thm)])).
29.16/4.86	tff('284', plain,
29.16/4.86	    ( '#form27'
29.16/4.86	     | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	        != ((??(cR)) <=> (!!(cS)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['283'])).
29.16/4.86	tff('285', plain, ( '#form27') <= (( '#form27')),
29.16/4.86	    inference('split', [status(esa)], ['284'])).
29.16/4.86	tff('286', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      != ((??(cR)) <=> (!!(cS))))
29.16/4.86	      <= (~
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['284'])).
29.16/4.86	tff('287', plain,
29.16/4.86	    ( '#form27'
29.16/4.86	     | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    define([status(thm)])).
29.16/4.86	tff('288', plain,
29.16/4.86	    (~ '#form27')
29.16/4.86	      <= (~
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('renaming', [status(thm)], ['286', '287'])).
29.16/4.86	tff('289', plain,
29.16/4.86	    ~ ( '#form27') | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['285', '288'])).
29.16/4.86	tff('290', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['27'])).
29.16/4.86	tff('291', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['37'])).
29.16/4.86	tff('292', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          (??(cS))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['164'])).
29.16/4.86	tff('293', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) != ($true <=> (??(cS))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['291', '292'])).
29.16/4.86	tff('294', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) != (??(cS)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['293'])).
29.16/4.86	tff('295', plain,
29.16/4.86	    (($true <=> ((!!(cQ)) <=> (??(cP)))) != (??(cS)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['290', '294'])).
29.16/4.86	tff('296', plain,
29.16/4.86	    (((!!(cQ)) <=> (??(cP))) != (??(cS)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['295'])).
29.16/4.86	tff('297', plain,
29.16/4.86	    (( ((!!(cQ)) <=> (??(cP))) |  (??(cS))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['296'])).
29.16/4.86	tff('298', plain,
29.16/4.86	    (((!!(cQ)) = (??(cP)) |  (??(cS))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['297'])).
29.16/4.86	tff('299', plain,
29.16/4.86	    ~ ( (!!(cP))) | 
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ( (??(cS))) | ((!!(cQ)) = (??(cP))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['298'])).
29.16/4.86	tff('300', plain,
29.16/4.86	    ~ ((!!(cP)) = (??(cS))) | 
29.16/4.86	    ~
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ~
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['268'])).
29.16/4.86	tff('301', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['268'])).
29.16/4.86	tff('302', plain,
29.16/4.86	    (( ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	        ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['301'])).
29.16/4.86	tff('303', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	       = ((!!(cQ)) <=> (??(cP)))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['302'])).
29.16/4.86	tff('304', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['303'])).
29.16/4.86	tff('305', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) != (??(cS)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['293'])).
29.16/4.86	tff('306', plain,
29.16/4.86	    (( ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	        ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      |  (??(cS))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['305'])).
29.16/4.86	tff('307', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	       = ((!!(cQ)) <=> (??(cP)))
29.16/4.86	      |  (??(cS))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['306'])).
29.16/4.86	tff('308', plain,
29.16/4.86	    ~ ( (!!(cP))) | 
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ( (??(cS))), inference('split', [status(esa)], ['307'])).
29.16/4.86	tff('309', plain, ( '#form13') <= (( '#form13')),
29.16/4.86	    inference('split', [status(esa)], ['143'])).
29.16/4.86	tff('310', plain, ( (!!(cR))) <= (( (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['146'])).
29.16/4.86	tff('311', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['139'])).
29.16/4.86	tff('312', plain,
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      <= (~
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['77'])).
29.16/4.86	tff('313', plain,
29.16/4.86	    (~ ((??(cQ)) <=> (!!(cR))))
29.16/4.86	      <= (~
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['311', '312'])).
29.16/4.86	tff('314', plain,
29.16/4.86	    ((??(cQ)) != (!!(cR)))
29.16/4.86	      <= (~
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['313'])).
29.16/4.86	tff('315', plain,
29.16/4.86	    (~ (??(cQ)))
29.16/4.86	      <= (~
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (!!(cR)))),
29.16/4.86	    inference('sup-', [status(thm)], ['310', '314'])).
29.16/4.86	tff('316', plain, ( '#form13' | ~ (??(cQ))), define([status(thm)])).
29.16/4.86	tff('317', plain,
29.16/4.86	    (~ '#form13')
29.16/4.86	      <= (~
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (!!(cR)))),
29.16/4.86	    inference('renaming', [status(thm)], ['315', '316'])).
29.16/4.86	tff('318', plain,
29.16/4.86	    ~ ( '#form13') | 
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ( (!!(cR))), inference('sup-', [status(thm)], ['309', '317'])).
29.16/4.86	tff('319', plain, ((!!(cP)) = (??(cS))) <= (((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['37'])).
29.16/4.86	tff('320', plain, ((~ (!!(cP)) |  (??(cS)))) <= (((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['319'])).
29.16/4.86	tff('321', plain, ~ ( (!!(cP))) | ~ ((!!(cP)) = (??(cS))) | ( (??(cS))),
29.16/4.86	    inference('split', [status(esa)], ['320'])).
29.16/4.86	tff('322', plain, ( (??(cQ))) <= (( (??(cQ)))),
29.16/4.86	    inference('split', [status(esa)], ['146'])).
29.16/4.86	tff('323', plain, ( cQ('#sk10')) <= (( (??(cQ)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['322'])).
29.16/4.86	tff('324', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['92'])).
29.16/4.86	tff('325', plain,
29.16/4.86	    ( (!!((^[Y0 : $i]: (cQ('#sk26') <=> cQ(Y0))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['324'])).
29.16/4.86	tff('326', plain,
29.16/4.86	    (![X1]:  (cQ('#sk26') <=> cQ(X1)))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['325'])).
29.16/4.86	tff('327', plain,
29.16/4.86	    (![X1]: cQ('#sk26') = cQ(X1))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['326'])).
29.16/4.86	tff('328', plain,
29.16/4.86	    (![X1]: cQ('#sk26') = cQ(X1))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['326'])).
29.16/4.86	tff('329', plain,
29.16/4.86	    (![X0, X1]: cQ(X0) = cQ(X1))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('sup+', [status(thm)], ['327', '328'])).
29.16/4.86	tff('330', plain, ( (??(cP))) <= (( (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['11'])).
29.16/4.86	tff('331', plain, ((!!(cQ)) != (??(cP))) <= (~ ((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['9'])).
29.16/4.86	tff('332', plain, (~ (!!(cQ))) <= (~ ((!!(cQ)) = (??(cP))) & ( (??(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['330', '331'])).
29.16/4.86	tff('333', plain, (~ cQ('#sk5')) <= (~ ((!!(cQ)) = (??(cP))) & ( (??(cP)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['332'])).
29.16/4.86	tff('334', plain,
29.16/4.86	    (![X0]: ~ cQ(X0))
29.16/4.86	      <= (~ ((!!(cQ)) = (??(cP))) & 
29.16/4.86	          ( (??(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['329', '333'])).
29.16/4.86	tff('335', plain,
29.16/4.86	    ~ ( (??(cP))) | ((!!(cQ)) = (??(cP))) | ~ ( (??(cQ))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['323', '334'])).
29.16/4.86	tff('336', plain,
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.16/4.86	    ~ ((!!(cQ)) = (??(cP))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['9'])).
29.16/4.86	tff('337', plain, ( (??(cS))) | ((!!(cP)) = (??(cS))) | ( (!!(cP))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('338', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('split', [status(esa)], ['15'])).
29.16/4.86	tff('339', plain, ( (!!(cP))) <= (( (!!(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('340', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	      ((??(cR)) <=> (!!(cS)))))
29.16/4.86	     != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	          ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('ho_norm', [status(thm)], ['0'])).
29.16/4.86	tff('341', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	           ($true <=> (??(cS))))))
29.16/4.86	      <= (( (!!(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['339', '340'])).
29.16/4.86	tff('342', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	           (??(cS)))))
29.16/4.86	      <= (( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['341'])).
29.16/4.86	tff('343', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != ((((!!(cQ)) <=> (??(cP))) <=> ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	           (??(cS)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['338', '342'])).
29.16/4.86	tff('344', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          (??(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['343'])).
29.16/4.86	tff('345', plain,
29.16/4.86	    (( ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          (??(cS)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['344'])).
29.16/4.86	tff('346', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS))))
29.16/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	         = (??(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['345'])).
29.16/4.86	tff('347', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) = (??(cS))) | 
29.16/4.86	    ~ ( (!!(cP))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['346'])).
29.16/4.86	tff('348', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['27'])).
29.16/4.86	tff('349', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) = (??(cS)))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['233'])).
29.16/4.86	tff('350', plain,
29.16/4.86	    (($true <=> ((!!(cQ)) <=> (??(cP)))) = (??(cS)))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('sup+', [status(thm)], ['348', '349'])).
29.16/4.86	tff('351', plain,
29.16/4.86	    (((!!(cQ)) <=> (??(cP))) = (??(cS)))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['350'])).
29.16/4.86	tff('352', plain,
29.16/4.86	    ((~ ((!!(cQ)) <=> (??(cP))) |  (??(cS))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['351'])).
29.16/4.86	tff('353', plain,
29.16/4.86	    (((!!(cQ)) != (??(cP)) |  (??(cS))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['352'])).
29.16/4.86	tff('354', plain,
29.16/4.86	    ~ ( (!!(cP))) | ~ ((!!(cQ)) = (??(cP))) | 
29.16/4.86	    ~
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ( (??(cS))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['353'])).
29.16/4.86	tff('355', plain, ( '#form13') <= (( '#form13')),
29.16/4.86	    inference('split', [status(esa)], ['143'])).
29.16/4.86	tff('356', plain,
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['150'])).
29.16/4.86	tff('357', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['139'])).
29.16/4.86	tff('358', plain,
29.16/4.86	    ( ((??(cQ)) <=> (!!(cR))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('sup+', [status(thm)], ['356', '357'])).
29.16/4.86	tff('359', plain,
29.16/4.86	    ((??(cQ)) = (!!(cR)))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['358'])).
29.16/4.86	tff('360', plain, (~ (!!(cR))) <= (~ ( (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['82'])).
29.16/4.86	tff('361', plain,
29.16/4.86	    (~ (??(cQ)))
29.16/4.86	      <= (~ ( (!!(cR))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['359', '360'])).
29.16/4.86	tff('362', plain, ( '#form13' | ~ (??(cQ))), define([status(thm)])).
29.16/4.86	tff('363', plain,
29.16/4.86	    (~ '#form13')
29.16/4.86	      <= (~ ( (!!(cR))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('renaming', [status(thm)], ['361', '362'])).
29.16/4.86	tff('364', plain,
29.16/4.86	    ~ ( '#form13') | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ( (!!(cR))), inference('sup-', [status(thm)], ['355', '363'])).
29.16/4.86	tff('365', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          (??(cS))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['164'])).
29.16/4.86	tff('366', plain,
29.16/4.86	    ((~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	         ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	           (??(cS)))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['365'])).
29.16/4.86	tff('367', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	       != ((!!(cQ)) <=> (??(cP)))
29.16/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	         != (??(cS))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['366'])).
29.16/4.86	tff('368', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) = (??(cS))) | 
29.16/4.86	    ~ ( (!!(cP))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['367'])).
29.16/4.86	tff('369', plain, ( '#form13') <= (( '#form13')),
29.16/4.86	    inference('split', [status(esa)], ['143'])).
29.16/4.86	tff('370', plain, (~ (??(cQ))) <= (~ ( (!!(cR))) & ((??(cQ)) = (!!(cR)))),
29.16/4.86	    inference('sup-', [status(thm)], ['140', '141'])).
29.16/4.86	tff('371', plain, ( '#form13' | ~ (??(cQ))), define([status(thm)])).
29.16/4.86	tff('372', plain, (~ '#form13') <= (~ ( (!!(cR))) & ((??(cQ)) = (!!(cR)))),
29.16/4.86	    inference('renaming', [status(thm)], ['370', '371'])).
29.16/4.86	tff('373', plain, ~ ( '#form13') | ~ ((??(cQ)) = (!!(cR))) | ( (!!(cR))),
29.16/4.86	    inference('sup-', [status(thm)], ['369', '372'])).
29.16/4.86	tff('374', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['150'])).
29.16/4.86	tff('375', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['92'])).
29.16/4.86	tff('376', plain,
29.16/4.86	    ( ((??(cR)) <=> (!!(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('sup+', [status(thm)], ['374', '375'])).
29.16/4.86	tff('377', plain,
29.16/4.86	    ((??(cR)) = (!!(cS)))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['376'])).
29.16/4.86	tff('378', plain, ( (??(cR))) <= (( (??(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['121'])).
29.16/4.86	tff('379', plain,
29.16/4.86	    ( (!!(cS)))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
29.16/4.86	          ( (??(cR)))),
29.16/4.86	    inference('sup+', [status(thm)], ['377', '378'])).
29.16/4.86	tff('380', plain, (~ '#form14' |  (!!(cS))), define([status(thm)])).
29.16/4.86	tff('381', plain,
29.16/4.86	    ( '#form14')
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
29.16/4.86	          ( (??(cR)))),
29.16/4.86	    inference('renaming', [status(thm)], ['379', '380'])).
29.16/4.86	tff('382', plain, (~ '#form14') <= (~ ( '#form14')),
29.16/4.86	    inference('split', [status(esa)], ['127'])).
29.16/4.86	tff('383', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.16/4.86	    ( '#form14') | ~ ( (??(cR))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['381', '382'])).
29.16/4.86	tff('384', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('split', [status(esa)], ['15'])).
29.16/4.86	tff('385', plain,
29.16/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      |  ((!!(cQ)) <=> (??(cP)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['384'])).
29.16/4.86	tff('386', plain,
29.16/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      | (!!(cQ)) = (??(cP))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['385'])).
29.16/4.86	tff('387', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ((!!(cQ)) = (??(cP))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['386'])).
29.16/4.86	tff('388', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('split', [status(esa)], ['15'])).
29.16/4.86	tff('389', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['111'])).
29.16/4.86	tff('390', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != ((((!!(cQ)) <=> (??(cP))) <=> ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['388', '389'])).
29.16/4.86	tff('391', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['390'])).
29.16/4.86	tff('392', plain,
29.16/4.86	    ((~ ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['391'])).
29.16/4.86	tff('393', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	           ((??(cR)) <=> (!!(cS))))
29.16/4.86	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['392'])).
29.16/4.86	tff('394', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ~ ((!!(cP)) = (??(cS))) | 
29.16/4.86	    ~
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))),
29.16/4.86	    inference('split', [status(esa)], ['393'])).
29.16/4.86	tff('395', plain, ((??(cR)) = (!!(cS))) <= (((??(cR)) = (!!(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['92'])).
29.16/4.86	tff('396', plain, ((??(cR)) != (!!(cS))) <= (~ ((??(cR)) = (!!(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['119'])).
29.16/4.86	tff('397', plain, ((~ (??(cR)) | ~ (!!(cS)))) <= (~ ((??(cR)) = (!!(cS)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['396'])).
29.16/4.86	tff('398', plain, (~ (??(cR))) <= (~ ( (??(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['397'])).
29.16/4.86	tff('399', plain, (~ (!!(cS))) <= (~ ( (??(cR))) & ((??(cR)) = (!!(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['395', '398'])).
29.16/4.86	tff('400', plain, ( '#form14' | ~ (!!(cS))), define([status(thm)])).
29.16/4.86	tff('401', plain, ( '#form14') <= (( '#form14')),
29.16/4.86	    inference('split', [status(esa)], ['400'])).
29.16/4.86	tff('402', plain, (~ (!!(cS))) <= (~ ( (!!(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['400'])).
29.16/4.86	tff('403', plain, ( '#form14' | ~ (!!(cS))), define([status(thm)])).
29.16/4.86	tff('404', plain, (~ '#form14') <= (~ ( (!!(cS)))),
29.16/4.86	    inference('renaming', [status(thm)], ['402', '403'])).
29.16/4.86	tff('405', plain, ~ ( '#form14') | ( (!!(cS))),
29.16/4.86	    inference('sup-', [status(thm)], ['401', '404'])).
29.16/4.86	tff('406', plain,
29.16/4.86	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['9'])).
29.16/4.86	tff('407', plain,
29.16/4.86	    (![X1]: ~ (!!((^[Y0 : $i]: (cS(X1) <=> cS(Y0))))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['406'])).
29.16/4.86	tff('408', plain,
29.16/4.86	    (![X1]: ~ (cS(X1) <=> cS('#sk15'(X1))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['407'])).
29.16/4.86	tff('409', plain,
29.16/4.86	    (![X1]: cS(X1) != cS('#sk15'(X1)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['408'])).
29.16/4.86	tff('410', plain,
29.16/4.86	    (![X1]: ( cS(X1) |  cS('#sk15'(X1))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['409'])).
29.16/4.86	tff('411', plain, (~ (??(cS))) <= (~ ( (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['194'])).
29.16/4.86	tff('412', plain, (![X1]: ~ cS(X1)) <= (~ ( (??(cS)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['411'])).
29.16/4.86	tff('413', plain,
29.16/4.86	    (![X0]:  cS(X0))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.16/4.86	          ~ ( (??(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['410', '412'])).
29.16/4.86	tff('414', plain, (![X1]: ~ cS(X1)) <= (~ ( (??(cS)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['411'])).
29.16/4.86	tff('415', plain,
29.16/4.86	    ( (??(cS))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['413', '414'])).
29.16/4.86	tff('416', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['114'])).
29.16/4.86	tff('417', plain,
29.16/4.86	    (( ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	        ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['416'])).
29.16/4.86	tff('418', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	       = ((!!(cQ)) <=> (??(cP)))
29.16/4.86	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['417'])).
29.16/4.86	tff('419', plain,
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ~
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['418'])).
29.16/4.86	tff('420', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) != (!!(cP)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['259'])).
29.16/4.86	tff('421', plain,
29.16/4.86	    (( ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	        ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      |  (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['420'])).
29.16/4.86	tff('422', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	       = ((!!(cQ)) <=> (??(cP)))
29.16/4.86	      |  (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['421'])).
29.16/4.86	tff('423', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ( (!!(cP))) | ~ ( (??(cS))), inference('split', [status(esa)], ['422'])).
29.16/4.86	tff('424', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (( (??(cS))) & ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['247'])).
29.16/4.86	tff('425', plain,
29.16/4.86	    (( ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      |  (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))))
29.16/4.86	      <= (( (??(cS))) & ( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['424'])).
29.16/4.86	tff('426', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS))))
29.16/4.86	      | ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	         ((!!(cQ)) <=> (??(cP))))
29.16/4.86	         = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (( (??(cS))) & ( (!!(cP)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['425'])).
29.16/4.86	tff('427', plain,
29.16/4.86	    ~ ( (!!(cP))) | ~ ( (??(cS))) | 
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))),
29.16/4.86	    inference('split', [status(esa)], ['426'])).
29.16/4.86	tff('428', plain,
29.16/4.86	    ((??(cQ)) = (!!(cR)))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['358'])).
29.16/4.86	tff('429', plain, ( (!!(cR))) <= (( (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['146'])).
29.16/4.86	tff('430', plain,
29.16/4.86	    ( (??(cQ)))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (!!(cR)))),
29.16/4.86	    inference('sup+', [status(thm)], ['428', '429'])).
29.16/4.86	tff('431', plain, ((??(cQ)) = (!!(cR))) <= (((??(cQ)) = (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['139'])).
29.16/4.86	tff('432', plain, ( (!!(cR))) <= (( (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['146'])).
29.16/4.86	tff('433', plain, ( (??(cQ))) <= (((??(cQ)) = (!!(cR))) & ( (!!(cR)))),
29.16/4.86	    inference('sup+', [status(thm)], ['431', '432'])).
29.16/4.86	tff('434', plain, (~ '#form13' |  (??(cQ))), define([status(thm)])).
29.16/4.86	tff('435', plain,
29.16/4.86	    ( '#form13')
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (!!(cR)))),
29.16/4.86	    inference('renaming', [status(thm)], ['430', '434'])).
29.16/4.86	tff('436', plain, (~ '#form13' |  (??(cQ))), define([status(thm)])).
29.16/4.86	tff('437', plain, (~ '#form13') <= (~ ( '#form13')),
29.16/4.86	    inference('split', [status(esa)], ['436'])).
29.16/4.86	tff('438', plain,
29.16/4.86	    ~ ( (!!(cR))) | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ( '#form13'), inference('sup-', [status(thm)], ['435', '437'])).
29.16/4.86	tff('439', plain, ( '#form13') <= (( '#form13')),
29.16/4.86	    inference('split', [status(esa)], ['143'])).
29.16/4.86	tff('440', plain, (~ (??(cQ))) <= (~ ( (??(cQ)))),
29.16/4.86	    inference('split', [status(esa)], ['143'])).
29.16/4.86	tff('441', plain, ( '#form13' | ~ (??(cQ))), define([status(thm)])).
29.16/4.86	tff('442', plain, (~ '#form13') <= (~ ( (??(cQ)))),
29.16/4.86	    inference('renaming', [status(thm)], ['440', '441'])).
29.16/4.86	tff('443', plain, ~ ( '#form13') | ( (??(cQ))),
29.16/4.86	    inference('sup-', [status(thm)], ['439', '442'])).
29.16/4.86	tff('444', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	          ((!!(cQ)) <=> (??(cP)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['102'])).
29.16/4.86	tff('445', plain,
29.16/4.86	    (( ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	          ((!!(cQ)) <=> (??(cP))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['444'])).
29.16/4.86	tff('446', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS))))
29.16/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	         = ((!!(cQ)) <=> (??(cP)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['445'])).
29.16/4.86	tff('447', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['446'])).
29.16/4.86	tff('448', plain,
29.16/4.86	    ((??(cQ)) != (!!(cR)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['153'])).
29.16/4.86	tff('449', plain,
29.16/4.86	    (( (??(cQ)) |  (!!(cR))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['448'])).
29.16/4.86	tff('450', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ( (??(cQ))) | ( (!!(cR))), inference('split', [status(esa)], ['449'])).
29.16/4.86	tff('451', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ((??(cQ)) = (!!(cR))), inference('split', [status(esa)], ['139'])).
29.16/4.86	tff('452', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ((!!(cP)) = (??(cS))), inference('split', [status(esa)], ['37'])).
29.16/4.86	tff('453', plain,
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['150'])).
29.16/4.86	tff('454', plain,
29.16/4.86	    ((~ ((??(cQ)) <=> (!!(cR)))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['453'])).
29.16/4.86	tff('455', plain,
29.16/4.86	    (((??(cQ)) != (!!(cR))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['454'])).
29.16/4.86	tff('456', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ((??(cQ)) = (!!(cR))), inference('split', [status(esa)], ['455'])).
29.16/4.86	tff('457', plain,
29.16/4.86	    ((??(cQ)) != (!!(cR)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['153'])).
29.16/4.86	tff('458', plain,
29.16/4.86	    ((~ (??(cQ)) | ~ (!!(cR))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['457'])).
29.16/4.86	tff('459', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ( (!!(cR))) | ~ ( (??(cQ))), inference('split', [status(esa)], ['458'])).
29.16/4.86	tff('460', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('split', [status(esa)], ['15'])).
29.16/4.86	tff('461', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	     ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	      ((??(cR)) <=> (!!(cS)))))
29.16/4.86	     != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	          ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('ho_norm', [status(thm)], ['0'])).
29.16/4.86	tff('462', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != ((((!!(cQ)) <=> (??(cP))) <=> ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	           ((!!(cP)) <=> (??(cS))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('sup-', [status(thm)], ['460', '461'])).
29.16/4.86	tff('463', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          ((!!(cP)) <=> (??(cS)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['462'])).
29.16/4.86	tff('464', plain,
29.16/4.86	    (( ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          ((!!(cP)) <=> (??(cS))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['463'])).
29.16/4.86	tff('465', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS))))
29.16/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	         = ((!!(cP)) <=> (??(cS)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['464'])).
29.16/4.86	tff('466', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['465'])).
29.16/4.86	tff('467', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['15'])).
29.16/4.86	tff('468', plain,
29.16/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      |  ((!!(cP)) <=> (??(cS)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['467'])).
29.16/4.86	tff('469', plain,
29.16/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      | (!!(cP)) = (??(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['468'])).
29.16/4.86	tff('470', plain,
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.16/4.86	    ((!!(cP)) = (??(cS))), inference('split', [status(esa)], ['469'])).
29.16/4.86	tff('471', plain, ((!!(cP)) = (??(cS))) <= (((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['37'])).
29.16/4.86	tff('472', plain, (( (!!(cP)) | ~ (??(cS)))) <= (((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['471'])).
29.16/4.86	tff('473', plain, ~ ((!!(cP)) = (??(cS))) | ~ ( (??(cS))) | ( (!!(cP))),
29.16/4.86	    inference('split', [status(esa)], ['472'])).
29.16/4.86	tff('474', plain, ( (!!(cP))) <= (( (!!(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('475', plain, (![X1]:  cP(X1)) <= (( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['474'])).
29.16/4.86	tff('476', plain,
29.16/4.86	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['80'])).
29.16/4.86	tff('477', plain,
29.16/4.86	    (![X1]: ~ (!!((^[Y0 : $i]: (cP(X1) <=> cP(Y0))))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['476'])).
29.16/4.86	tff('478', plain,
29.16/4.86	    (![X1]: ~ (cP(X1) <=> cP('#sk23'(X1))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['477'])).
29.16/4.86	tff('479', plain,
29.16/4.86	    (![X1]: cP(X1) != cP('#sk23'(X1)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['478'])).
29.16/4.86	tff('480', plain,
29.16/4.86	    (![X0]: ~ cP(X0))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['475', '479'])).
29.16/4.86	tff('481', plain, (![X1]:  cP(X1)) <= (( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['474'])).
29.16/4.86	tff('482', plain,
29.16/4.86	    ~ ( (!!(cP))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))),
29.16/4.86	    inference('demod', [status(thm)], ['480', '481'])).
29.16/4.86	tff('483', plain,
29.16/4.86	    ((!!(cQ)) != (??(cP)))
29.16/4.86	      <= (~
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['30'])).
29.16/4.86	tff('484', plain,
29.16/4.86	    ((~ (!!(cQ)) | ~ (??(cP))))
29.16/4.86	      <= (~
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['483'])).
29.16/4.86	tff('485', plain,
29.16/4.86	    ~ ( (??(cP))) | ~ ( (!!(cQ))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['484'])).
29.16/4.86	tff('486', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['390'])).
29.16/4.86	tff('487', plain,
29.16/4.86	    (( ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['486'])).
29.16/4.86	tff('488', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS))))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['487'])).
29.16/4.86	tff('489', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ~ ((!!(cP)) = (??(cS))), inference('split', [status(esa)], ['488'])).
29.16/4.86	tff('490', plain, ( (!!(cP))) <= (( (!!(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('491', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['257'])).
29.16/4.86	tff('492', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          $true))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['490', '491'])).
29.16/4.86	tff('493', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['492'])).
29.16/4.86	tff('494', plain,
29.16/4.86	    (( ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	        ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['493'])).
29.16/4.86	tff('495', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	       = ((!!(cQ)) <=> (??(cP)))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (!!(cP)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['494'])).
29.16/4.86	tff('496', plain,
29.16/4.86	    ~ ( (!!(cP))) | ~ ( (??(cS))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))),
29.16/4.86	    inference('split', [status(esa)], ['495'])).
29.16/4.86	tff('497', plain,
29.16/4.86	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['19'])).
29.16/4.86	tff('498', plain,
29.16/4.86	    (![X1]: ~ (!!((^[Y0 : $i]: (cR(Y0) <=> cR(X1))))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['497'])).
29.16/4.86	tff('499', plain,
29.16/4.86	    (![X1]: ~ (cR('#sk4'(X1)) <=> cR(X1)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['498'])).
29.16/4.86	tff('500', plain,
29.16/4.86	    (![X1]: cR('#sk4'(X1)) != cR(X1))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['499'])).
29.16/4.86	tff('501', plain,
29.16/4.86	    (![X1]: ( cR('#sk4'(X1)) |  cR(X1)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['500'])).
29.16/4.86	tff('502', plain, (~ (??(cR))) <= (~ ( (??(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['397'])).
29.16/4.86	tff('503', plain, (![X1]: ~ cR(X1)) <= (~ ( (??(cR)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['502'])).
29.16/4.86	tff('504', plain,
29.16/4.86	    (![X0]:  cR(X0))
29.16/4.86	      <= (~ ( (??(cR))) & 
29.16/4.86	          ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['501', '503'])).
29.16/4.86	tff('505', plain, (![X1]: ~ cR(X1)) <= (~ ( (??(cR)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['502'])).
29.16/4.86	tff('506', plain,
29.16/4.86	    ( (??(cR))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['504', '505'])).
29.16/4.86	tff('507', plain, ( (??(cS))) <= (( (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('508', plain,
29.16/4.86	    (((!!(cQ)) <=> (??(cP))) = (??(cS)))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['350'])).
29.16/4.86	tff('509', plain,
29.16/4.86	    ( ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('sup+', [status(thm)], ['507', '508'])).
29.16/4.86	tff('510', plain,
29.16/4.86	    ((!!(cQ)) = (??(cP)))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['509'])).
29.16/4.86	tff('511', plain,
29.16/4.86	    (( (!!(cQ)) | ~ (??(cP))))
29.16/4.86	      <= ((((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['510'])).
29.16/4.86	tff('512', plain,
29.16/4.86	    ~ ( (!!(cP))) | ~ ( (??(cS))) | 
29.16/4.86	    ~
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.16/4.86	    ( (!!(cQ))) | ~ ( (??(cP))), inference('split', [status(esa)], ['511'])).
29.16/4.86	tff('513', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['150'])).
29.16/4.86	tff('514', plain,
29.16/4.86	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['119'])).
29.16/4.86	tff('515', plain,
29.16/4.86	    (~ ((??(cR)) <=> (!!(cS))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('sup-', [status(thm)], ['513', '514'])).
29.16/4.86	tff('516', plain,
29.16/4.86	    ((??(cR)) != (!!(cS)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['515'])).
29.16/4.86	tff('517', plain,
29.16/4.86	    (( (??(cR)) |  (!!(cS))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['516'])).
29.16/4.86	tff('518', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.16/4.86	    ( (!!(cS))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
29.16/4.86	    ( (??(cR))), inference('split', [status(esa)], ['517'])).
29.16/4.86	tff('519', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))) | 
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['132'])).
29.16/4.86	tff('520', plain,
29.16/4.86	    ((??(cR)) = (!!(cS)))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['376'])).
29.16/4.86	tff('521', plain,
29.16/4.86	    (( (??(cR)) | ~ (!!(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['520'])).
29.16/4.86	tff('522', plain,
29.16/4.86	    ~ ( (!!(cS))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.16/4.86	    ( (??(cR))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['521'])).
29.16/4.86	tff('523', plain,
29.16/4.86	    ((??(cQ)) = (!!(cR)))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['358'])).
29.16/4.86	tff('524', plain,
29.16/4.86	    ((~ (??(cQ)) |  (!!(cR))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['523'])).
29.16/4.86	tff('525', plain,
29.16/4.86	    ~ ( (??(cQ))) | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ( (!!(cR))), inference('split', [status(esa)], ['524'])).
29.16/4.86	tff('526', plain, ((??(cQ)) = (!!(cR))) <= (((??(cQ)) = (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['139'])).
29.16/4.86	tff('527', plain, (( (??(cQ)) | ~ (!!(cR)))) <= (((??(cQ)) = (!!(cR)))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['526'])).
29.16/4.86	tff('528', plain, ~ ( (!!(cR))) | ~ ((??(cQ)) = (!!(cR))) | ( (??(cQ))),
29.16/4.86	    inference('split', [status(esa)], ['527'])).
29.16/4.86	tff('529', plain, ( (??(cR))) | ((??(cR)) = (!!(cS))) | ( (!!(cS))),
29.16/4.86	    inference('split', [status(esa)], ['121'])).
29.16/4.86	tff('530', plain, ( (!!(cQ))) <= (( (!!(cQ)))),
29.16/4.86	    inference('split', [status(esa)], ['11'])).
29.16/4.86	tff('531', plain, (![X1]:  cQ(X1)) <= (( (!!(cQ)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['530'])).
29.16/4.86	tff('532', plain, (~ (??(cQ))) <= (~ ( (??(cQ)))),
29.16/4.86	    inference('split', [status(esa)], ['82'])).
29.16/4.86	tff('533', plain, (![X1]: ~ cQ(X1)) <= (~ ( (??(cQ)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['532'])).
29.16/4.86	tff('534', plain, ~ ( (!!(cQ))) | ( (??(cQ))),
29.16/4.86	    inference('sup-', [status(thm)], ['531', '533'])).
29.16/4.86	tff('535', plain, ~ ( (!!(cS))) | ~ ( (??(cR))) | ((??(cR)) = (!!(cS))),
29.16/4.86	    inference('split', [status(esa)], ['397'])).
29.16/4.86	tff('536', plain, ((??(cQ)) = (!!(cR))) <= (((??(cQ)) = (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['139'])).
29.16/4.86	tff('537', plain, ((~ (??(cQ)) |  (!!(cR)))) <= (((??(cQ)) = (!!(cR)))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['536'])).
29.16/4.86	tff('538', plain, ~ ( (??(cQ))) | ~ ((??(cQ)) = (!!(cR))) | ( (!!(cR))),
29.16/4.86	    inference('split', [status(esa)], ['537'])).
29.16/4.86	tff('539', plain,
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['150'])).
29.16/4.86	tff('540', plain,
29.16/4.86	    (( ((??(cQ)) <=> (!!(cR)))
29.16/4.86	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['539'])).
29.16/4.86	tff('541', plain,
29.16/4.86	    (((??(cQ)) = (!!(cR))
29.16/4.86	      | ~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['540'])).
29.16/4.86	tff('542', plain,
29.16/4.86	    ((??(cQ)) = (!!(cR))) | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['541'])).
29.16/4.86	tff('543', plain,
29.16/4.86	    ~ ((??(cR)) = (!!(cS))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['119'])).
29.16/4.86	tff('544', plain, ((??(cR)) = (!!(cS))) <= (((??(cR)) = (!!(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['92'])).
29.16/4.86	tff('545', plain, (( (??(cR)) | ~ (!!(cS)))) <= (((??(cR)) = (!!(cS)))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['544'])).
29.16/4.86	tff('546', plain, ~ ( (!!(cS))) | ( (??(cR))) | ~ ((??(cR)) = (!!(cS))),
29.16/4.86	    inference('split', [status(esa)], ['545'])).
29.16/4.86	tff('547', plain, (![X1]:  cQ(X1)) <= (( (!!(cQ)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['530'])).
29.16/4.86	tff('548', plain, ( (!!(cR))) <= (( (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['146'])).
29.16/4.86	tff('549', plain, ((??(cQ)) != (!!(cR))) <= (~ ((??(cQ)) = (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['80'])).
29.16/4.86	tff('550', plain, (~ (??(cQ))) <= (~ ((??(cQ)) = (!!(cR))) & ( (!!(cR)))),
29.16/4.86	    inference('sup-', [status(thm)], ['548', '549'])).
29.16/4.86	tff('551', plain,
29.16/4.86	    (![X1]: ~ cQ(X1)) <= (~ ((??(cQ)) = (!!(cR))) & ( (!!(cR)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['550'])).
29.16/4.86	tff('552', plain, ~ ( (!!(cQ))) | ((??(cQ)) = (!!(cR))) | ~ ( (!!(cR))),
29.16/4.86	    inference('sup-', [status(thm)], ['547', '551'])).
29.16/4.86	tff('553', plain, ( (??(cR))) <= (( (??(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['121'])).
29.16/4.86	tff('554', plain, ( cR('#sk12')) <= (( (??(cR)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['553'])).
29.16/4.86	tff('555', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['37'])).
29.16/4.86	tff('556', plain,
29.16/4.86	    ( (!!((^[Y0 : $i]: (cR(Y0) <=> cR('#sk8'))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['555'])).
29.16/4.86	tff('557', plain,
29.16/4.86	    (![X1]:  (cR(X1) <=> cR('#sk8')))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['556'])).
29.16/4.86	tff('558', plain,
29.16/4.86	    (![X1]: cR(X1) = cR('#sk8'))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['557'])).
29.16/4.86	tff('559', plain,
29.16/4.86	    (![X1]: cR(X1) = cR('#sk8'))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['557'])).
29.16/4.86	tff('560', plain, (~ (!!(cR))) <= (~ ( (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['82'])).
29.16/4.86	tff('561', plain, (~ cR('#sk9')) <= (~ ( (!!(cR)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['560'])).
29.16/4.86	tff('562', plain,
29.16/4.86	    (~ cR('#sk8'))
29.16/4.86	      <= (~ ( (!!(cR))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['559', '561'])).
29.16/4.86	tff('563', plain,
29.16/4.86	    (![X0]: ~ cR(X0))
29.16/4.86	      <= (~ ( (!!(cR))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['558', '562'])).
29.16/4.86	tff('564', plain,
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ( (!!(cR))) | ~ ( (??(cR))),
29.16/4.86	    inference('sup-', [status(thm)], ['554', '563'])).
29.16/4.86	tff('565', plain,
29.16/4.86	    ((!!(cQ)) = (??(cP)))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['49'])).
29.16/4.86	tff('566', plain,
29.16/4.86	    (( (!!(cQ)) | ~ (??(cP))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['565'])).
29.16/4.86	tff('567', plain,
29.16/4.86	    ~ ( (??(cP))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ( (!!(cQ))), inference('split', [status(esa)], ['566'])).
29.16/4.86	tff('568', plain,
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ((??(cQ)) = (!!(cR))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['80'])).
29.16/4.86	tff('569', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['150'])).
29.16/4.86	tff('570', plain,
29.16/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      |  ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['569'])).
29.16/4.86	tff('571', plain,
29.16/4.86	    ((~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      | (??(cR)) = (!!(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['570'])).
29.16/4.86	tff('572', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.16/4.86	    ((??(cR)) = (!!(cS))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['571'])).
29.16/4.86	tff('573', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['77'])).
29.16/4.86	tff('574', plain,
29.16/4.86	    ((!!(cQ)) != (??(cP)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['55'])).
29.16/4.86	tff('575', plain,
29.16/4.86	    ((~ (!!(cQ)) | ~ (??(cP))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['574'])).
29.16/4.86	tff('576', plain,
29.16/4.86	    ~ ( (??(cP))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ~ ( (!!(cQ))), inference('split', [status(esa)], ['575'])).
29.16/4.86	tff('577', plain,
29.16/4.86	    ((??(cQ)) != (!!(cR)))
29.16/4.86	      <= (~
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['313'])).
29.16/4.86	tff('578', plain,
29.16/4.86	    ((~ (??(cQ)) | ~ (!!(cR))))
29.16/4.86	      <= (~
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['577'])).
29.16/4.86	tff('579', plain,
29.16/4.86	    ~ ( (??(cQ))) | 
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ( (!!(cR))), inference('split', [status(esa)], ['578'])).
29.16/4.86	tff('580', plain, ( '#form27') <= (( '#form27')),
29.16/4.86	    inference('split', [status(esa)], ['284'])).
29.16/4.86	tff('581', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      != ((??(cR)) <=> (!!(cS))))
29.16/4.86	      <= (~
29.16/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['281'])).
29.16/4.86	tff('582', plain,
29.16/4.86	    ( '#form27'
29.16/4.86	     | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    define([status(thm)])).
29.16/4.86	tff('583', plain,
29.16/4.86	    (~ '#form27')
29.16/4.86	      <= (~
29.16/4.86	          ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('renaming', [status(thm)], ['581', '582'])).
29.16/4.86	tff('584', plain,
29.16/4.86	    ~ ( '#form27') | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('sup-', [status(thm)], ['580', '583'])).
29.16/4.86	tff('585', plain, (![X1]:  cQ(X1)) <= (( (!!(cQ)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['530'])).
29.16/4.86	tff('586', plain,
29.16/4.86	    (~ (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['119'])).
29.16/4.86	tff('587', plain,
29.16/4.86	    (![X1]: ~ (!!((^[Y0 : $i]: (cQ(X1) <=> cQ(Y0))))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['586'])).
29.16/4.86	tff('588', plain,
29.16/4.86	    (![X1]: ~ (cQ(X1) <=> cQ('#sk33'(X1))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['587'])).
29.16/4.86	tff('589', plain,
29.16/4.86	    (![X1]: cQ(X1) != cQ('#sk33'(X1)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['588'])).
29.16/4.86	tff('590', plain,
29.16/4.86	    (![X0]: ~ cQ(X0))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
29.16/4.86	          ( (!!(cQ)))),
29.16/4.86	    inference('sup-', [status(thm)], ['585', '589'])).
29.16/4.86	tff('591', plain, (![X1]:  cQ(X1)) <= (( (!!(cQ)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['530'])).
29.16/4.86	tff('592', plain,
29.16/4.86	    ~ ( (!!(cQ))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
29.16/4.86	    inference('demod', [status(thm)], ['590', '591'])).
29.16/4.86	tff('593', plain,
29.16/4.86	    ((??(cR)) = (!!(cS)))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['376'])).
29.16/4.86	tff('594', plain,
29.16/4.86	    ((~ (??(cR)) |  (!!(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['593'])).
29.16/4.86	tff('595', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.16/4.86	    ( (!!(cS))) | ~ ( (??(cR))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['594'])).
29.16/4.86	tff('596', plain, ((!!(cQ)) = (??(cP))) <= (((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['27'])).
29.16/4.86	tff('597', plain, ((!!(cQ)) != (??(cP))) <= (~ ((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['9'])).
29.16/4.86	tff('598', plain, ((~ (!!(cQ)) | ~ (??(cP)))) <= (~ ((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['597'])).
29.16/4.86	tff('599', plain, (~ (??(cP))) <= (~ ( (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['598'])).
29.16/4.86	tff('600', plain, (~ (!!(cQ))) <= (~ ( (??(cP))) & ((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['596', '599'])).
29.16/4.86	tff('601', plain, ( '#form7' | ~ (!!(cQ))), define([status(thm)])).
29.16/4.86	tff('602', plain, ( '#form7') <= (( '#form7')),
29.16/4.86	    inference('split', [status(esa)], ['601'])).
29.16/4.86	tff('603', plain,
29.16/4.86	    ((!!(cQ)) = (??(cP)))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['49'])).
29.16/4.86	tff('604', plain, (~ (??(cP))) <= (~ ( (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['598'])).
29.16/4.86	tff('605', plain,
29.16/4.86	    (~ (!!(cQ)))
29.16/4.86	      <= (~ ( (??(cP))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['603', '604'])).
29.16/4.86	tff('606', plain, ( '#form7' | ~ (!!(cQ))), define([status(thm)])).
29.16/4.86	tff('607', plain,
29.16/4.86	    (~ '#form7')
29.16/4.86	      <= (~ ( (??(cP))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	            = ((!!(cQ)) <=> (??(cP)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('renaming', [status(thm)], ['605', '606'])).
29.16/4.86	tff('608', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ~ ( '#form7') | ( (??(cP))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['602', '607'])).
29.16/4.86	tff('609', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['15'])).
29.16/4.86	tff('610', plain, ( (??(cS))) <= (( (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('611', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['27'])).
29.16/4.86	tff('612', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['15'])).
29.16/4.86	tff('613', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	          (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['257'])).
29.16/4.86	tff('614', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) != (((!!(cP)) <=> (??(cS))) <=> (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['612', '613'])).
29.16/4.86	tff('615', plain,
29.16/4.86	    (($true <=> ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      != (((!!(cP)) <=> (??(cS))) <=> (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['611', '614'])).
29.16/4.86	tff('616', plain,
29.16/4.86	    (((!!(cQ)) <=> (??(cP))) != (((!!(cP)) <=> (??(cS))) <=> (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['615'])).
29.16/4.86	tff('617', plain,
29.16/4.86	    (((!!(cQ)) <=> (??(cP))) != (((!!(cP)) <=> $true) <=> (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['610', '616'])).
29.16/4.86	tff('618', plain,
29.16/4.86	    (~ ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['617'])).
29.16/4.86	tff('619', plain,
29.16/4.86	    ((!!(cQ)) != (??(cP)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['618'])).
29.16/4.86	tff('620', plain,
29.16/4.86	    ((~ (!!(cQ)) | ~ (??(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['619'])).
29.16/4.86	tff('621', plain,
29.16/4.86	    ~ ( (??(cP))) | ~ ( (??(cS))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.16/4.86	    ~ ( (!!(cQ))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['620'])).
29.16/4.86	tff('622', plain,
29.16/4.86	    ((!!(cP)) = (??(cS)))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['39'])).
29.16/4.86	tff('623', plain,
29.16/4.86	    (( (!!(cP)) | ~ (??(cS))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['622'])).
29.16/4.86	tff('624', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ( (!!(cP))) | ~ ( (??(cS))), inference('split', [status(esa)], ['623'])).
29.16/4.86	tff('625', plain, (![X1]:  cP(X1)) <= (( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['474'])).
29.16/4.86	tff('626', plain, (~ (??(cP))) <= (~ ( (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['598'])).
29.16/4.86	tff('627', plain, (![X1]: ~ cP(X1)) <= (~ ( (??(cP)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['626'])).
29.16/4.86	tff('628', plain, ~ ( (!!(cP))) | ( (??(cP))),
29.16/4.86	    inference('sup-', [status(thm)], ['625', '627'])).
29.16/4.86	tff('629', plain, ~ ( (!!(cQ))) | ( '#form7'),
29.16/4.86	    inference('split', [status(esa)], ['601'])).
29.16/4.86	tff('630', plain,
29.16/4.86	    ((??(cR)) != (!!(cS)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['515'])).
29.16/4.86	tff('631', plain,
29.16/4.86	    ((~ (??(cR)) | ~ (!!(cS))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
29.16/4.86	          ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	            = ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['630'])).
29.16/4.86	tff('632', plain,
29.16/4.86	    ~ ( (!!(cS))) | ~ ( (??(cR))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))),
29.16/4.86	    inference('split', [status(esa)], ['631'])).
29.16/4.86	tff('633', plain, ( (!!(cS))) <= (( (!!(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['121'])).
29.16/4.86	tff('634', plain, (![X1]:  cS(X1)) <= (( (!!(cS)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['633'])).
29.16/4.86	tff('635', plain,
29.16/4.86	    (![X1]: cS(X1) != cS('#sk15'(X1)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['408'])).
29.16/4.86	tff('636', plain,
29.16/4.86	    (![X0]: ~ cS(X0))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.16/4.86	          ( (!!(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['634', '635'])).
29.16/4.86	tff('637', plain, (![X1]:  cS(X1)) <= (( (!!(cS)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['633'])).
29.16/4.86	tff('638', plain,
29.16/4.86	    ~ ( (!!(cS))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))),
29.16/4.86	    inference('demod', [status(thm)], ['636', '637'])).
29.16/4.86	tff('639', plain, (![X1]:  cS(X1)) <= (( (!!(cS)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['633'])).
29.16/4.86	tff('640', plain, (![X1]: ~ cS(X1)) <= (~ ( (??(cS)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['411'])).
29.16/4.86	tff('641', plain, ( (??(cS))) | ~ ( (!!(cS))),
29.16/4.86	    inference('sup-', [status(thm)], ['639', '640'])).
29.16/4.86	tff('642', plain,
29.16/4.86	    ((??(cQ)) = (!!(cR)))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['358'])).
29.16/4.86	tff('643', plain,
29.16/4.86	    (( (??(cQ)) | ~ (!!(cR))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['642'])).
29.16/4.86	tff('644', plain,
29.16/4.86	    ~ ( (!!(cR))) | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ( (??(cQ))), inference('split', [status(esa)], ['643'])).
29.16/4.86	tff('645', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.16/4.86	    inference('split', [status(esa)], ['132'])).
29.16/4.86	tff('646', plain,
29.16/4.86	    (( (((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	        (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	           ((??(cR)) <=> (!!(cS))))))
29.16/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['645'])).
29.16/4.86	tff('647', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	       = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))
29.16/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	         != ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['646'])).
29.16/4.86	tff('648', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ~
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['647'])).
29.16/4.86	tff('649', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	          ((!!(cQ)) <=> (??(cP)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['102'])).
29.16/4.86	tff('650', plain,
29.16/4.86	    ((~ ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	         ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      | ~ ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['649'])).
29.16/4.86	tff('651', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	           ((??(cR)) <=> (!!(cS))))
29.16/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	         != ((!!(cQ)) <=> (??(cP)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['650'])).
29.16/4.86	tff('652', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.16/4.86	    ~
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['651'])).
29.16/4.86	tff('653', plain, ((!!(cQ)) = (??(cP))) <= (((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['27'])).
29.16/4.86	tff('654', plain, (( (!!(cQ)) | ~ (??(cP)))) <= (((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('lazy_cnf_equiv', [status(thm)], ['653'])).
29.16/4.86	tff('655', plain, ~ ( (??(cP))) | ~ ((!!(cQ)) = (??(cP))) | ( (!!(cQ))),
29.16/4.86	    inference('split', [status(esa)], ['654'])).
29.16/4.86	tff('656', plain,
29.16/4.86	    ~ ((!!(cP)) = (??(cS))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['19'])).
29.16/4.86	tff('657', plain, ( (!!(cR))) <= (( (!!(cR)))),
29.16/4.86	    inference('split', [status(esa)], ['146'])).
29.16/4.86	tff('658', plain, (![X1]:  cR(X1)) <= (( (!!(cR)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['657'])).
29.16/4.86	tff('659', plain, (![X1]: ~ cR(X1)) <= (~ ( (??(cR)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['502'])).
29.16/4.86	tff('660', plain, ( (??(cR))) | ~ ( (!!(cR))),
29.16/4.86	    inference('sup-', [status(thm)], ['658', '659'])).
29.16/4.86	tff('661', plain,
29.16/4.86	    (![X1]: cQ(X1) != cQ('#sk33'(X1)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['588'])).
29.16/4.86	tff('662', plain,
29.16/4.86	    (![X1]: ( cQ(X1) |  cQ('#sk33'(X1))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['661'])).
29.16/4.86	tff('663', plain, (![X1]: ~ cQ(X1)) <= (~ ( (??(cQ)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['532'])).
29.16/4.86	tff('664', plain,
29.16/4.86	    (![X0]:  cQ(X0))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) & 
29.16/4.86	          ~ ( (??(cQ)))),
29.16/4.86	    inference('sup-', [status(thm)], ['662', '663'])).
29.16/4.86	tff('665', plain, (![X1]: ~ cQ(X1)) <= (~ ( (??(cQ)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['532'])).
29.16/4.86	tff('666', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
29.16/4.86	    ( (??(cQ))), inference('sup-', [status(thm)], ['664', '665'])).
29.16/4.86	tff('667', plain, ( (??(cP))) <= (( (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['11'])).
29.16/4.86	tff('668', plain, ( cP('#sk6')) <= (( (??(cP)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['667'])).
29.16/4.86	tff('669', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['139'])).
29.16/4.86	tff('670', plain,
29.16/4.86	    ( (!!((^[Y0 : $i]: (cP('#sk20') <=> cP(Y0))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['669'])).
29.16/4.86	tff('671', plain,
29.16/4.86	    (![X1]:  (cP('#sk20') <=> cP(X1)))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['670'])).
29.16/4.86	tff('672', plain,
29.16/4.86	    (![X1]: cP('#sk20') = cP(X1))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['671'])).
29.16/4.86	tff('673', plain,
29.16/4.86	    (![X1]: cP('#sk20') = cP(X1))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['671'])).
29.16/4.86	tff('674', plain,
29.16/4.86	    (![X0, X1]: cP(X0) = cP(X1))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('sup+', [status(thm)], ['672', '673'])).
29.16/4.86	tff('675', plain, (~ (!!(cP))) <= (~ ( (!!(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['194'])).
29.16/4.86	tff('676', plain, (~ cP('#sk1')) <= (~ ( (!!(cP)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['675'])).
29.16/4.86	tff('677', plain,
29.16/4.86	    (![X0]: ~ cP(X0))
29.16/4.86	      <= (~ ( (!!(cP))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['674', '676'])).
29.16/4.86	tff('678', plain,
29.16/4.86	    ~ ( (??(cP))) | ( (!!(cP))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['668', '677'])).
29.16/4.86	tff('679', plain, ( cP('#sk6')) <= (( (??(cP)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['667'])).
29.16/4.86	tff('680', plain,
29.16/4.86	    (![X0, X1]: cP(X0) = cP(X1))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('sup+', [status(thm)], ['672', '673'])).
29.16/4.86	tff('681', plain, ( (??(cS))) <= (( (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['61'])).
29.16/4.86	tff('682', plain, ((!!(cP)) != (??(cS))) <= (~ ((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['19'])).
29.16/4.86	tff('683', plain, (~ (!!(cP))) <= (~ ((!!(cP)) = (??(cS))) & ( (??(cS)))),
29.16/4.86	    inference('sup-', [status(thm)], ['681', '682'])).
29.16/4.86	tff('684', plain, (~ cP('#sk1')) <= (~ ((!!(cP)) = (??(cS))) & ( (??(cS)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['683'])).
29.16/4.86	tff('685', plain,
29.16/4.86	    (![X0]: ~ cP(X0))
29.16/4.86	      <= (~ ((!!(cP)) = (??(cS))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['680', '684'])).
29.16/4.86	tff('686', plain,
29.16/4.86	    ~ ( (??(cP))) | ~ ( (??(cS))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ((!!(cP)) = (??(cS))), inference('sup-', [status(thm)], ['679', '685'])).
29.16/4.86	tff('687', plain, ( cS('#sk2')) <= (( (??(cS)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['207'])).
29.16/4.86	tff('688', plain,
29.16/4.86	    (![X0, X1]: cS(X0) = cS(X1))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('sup+', [status(thm)], ['212', '213'])).
29.16/4.86	tff('689', plain, (~ (!!(cS))) <= (~ ( (!!(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['397'])).
29.16/4.86	tff('690', plain, (~ cS('#sk11')) <= (~ ( (!!(cS)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['689'])).
29.16/4.86	tff('691', plain,
29.16/4.86	    (![X0]: ~ cS(X0))
29.16/4.86	      <= (~ ( (!!(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['688', '690'])).
29.16/4.86	tff('692', plain,
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.16/4.86	    ( (!!(cS))) | ~ ( (??(cS))),
29.16/4.86	    inference('sup-', [status(thm)], ['687', '691'])).
29.16/4.86	tff('693', plain,
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))) | 
29.16/4.86	    ( '#form27'), inference('split', [status(esa)], ['284'])).
29.16/4.86	tff('694', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['37'])).
29.16/4.86	tff('695', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))))
29.16/4.86	      <= (((!!(cP)) = (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['111'])).
29.16/4.86	tff('696', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	           ((!!(cQ)) <=> (??(cP)))) <=>
29.16/4.86	          $true))
29.16/4.86	      <= (((!!(cP)) = (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['694', '695'])).
29.16/4.86	tff('697', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	          ((!!(cQ)) <=> (??(cP)))))
29.16/4.86	      <= (((!!(cP)) = (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['696'])).
29.16/4.86	tff('698', plain,
29.16/4.86	    (( ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	          ((!!(cQ)) <=> (??(cP))))))
29.16/4.86	      <= (((!!(cP)) = (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['697'])).
29.16/4.86	tff('699', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS))))
29.16/4.86	      | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	         = ((!!(cQ)) <=> (??(cP)))))
29.16/4.86	      <= (((!!(cP)) = (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['698'])).
29.16/4.86	tff('700', plain,
29.16/4.86	    ~ ((!!(cP)) = (??(cS))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))) | 
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['699'])).
29.16/4.86	tff('701', plain, ( (??(cP))) <= (( (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['11'])).
29.16/4.86	tff('702', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['27'])).
29.16/4.86	tff('703', plain,
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP)))) != (!!(cP)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['259'])).
29.16/4.86	tff('704', plain,
29.16/4.86	    (($true <=> ((!!(cQ)) <=> (??(cP)))) != (!!(cP)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['702', '703'])).
29.16/4.86	tff('705', plain,
29.16/4.86	    (((!!(cQ)) <=> (??(cP))) != (!!(cP)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['704'])).
29.16/4.86	tff('706', plain,
29.16/4.86	    (((!!(cQ)) <=> $true) != (!!(cP)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.16/4.86	          ( (??(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['701', '705'])).
29.16/4.86	tff('707', plain,
29.16/4.86	    ((!!(cQ)) != (!!(cP)))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.16/4.86	          ( (??(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['706'])).
29.16/4.86	tff('708', plain,
29.16/4.86	    (( (!!(cQ)) |  (!!(cP))))
29.16/4.86	      <= (~
29.16/4.86	          (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	            ((!!(cQ)) <=> (??(cP))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	               ((!!(cP)) <=> (??(cS))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (??(cS))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) & 
29.16/4.86	          ( (??(cP)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['707'])).
29.16/4.86	tff('709', plain,
29.16/4.86	    ~ ( (??(cP))) | ~ ( (??(cS))) | ( (!!(cP))) | ( (!!(cQ))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['708'])).
29.16/4.86	tff('710', plain,
29.16/4.86	    (![X1]: cP(X1) != cP('#sk23'(X1)))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['478'])).
29.16/4.86	tff('711', plain,
29.16/4.86	    (![X1]: ( cP(X1) |  cP('#sk23'(X1))))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['710'])).
29.16/4.86	tff('712', plain, (![X1]: ~ cP(X1)) <= (~ ( (??(cP)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['626'])).
29.16/4.86	tff('713', plain,
29.16/4.86	    (![X0]:  cP(X0))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ~ ( (??(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['711', '712'])).
29.16/4.86	tff('714', plain, (![X1]: ~ cP(X1)) <= (~ ( (??(cP)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['626'])).
29.16/4.86	tff('715', plain,
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ( (??(cP))), inference('sup-', [status(thm)], ['713', '714'])).
29.16/4.86	tff('716', plain, ( cQ('#sk10')) <= (( (??(cQ)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['322'])).
29.16/4.86	tff('717', plain,
29.16/4.86	    (![X0, X1]: cQ(X0) = cQ(X1))
29.16/4.86	      <= (( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('sup+', [status(thm)], ['327', '328'])).
29.16/4.86	tff('718', plain, (~ (!!(cQ))) <= (~ ( (!!(cQ)))),
29.16/4.86	    inference('split', [status(esa)], ['598'])).
29.16/4.86	tff('719', plain, (~ cQ('#sk5')) <= (~ ( (!!(cQ)))),
29.16/4.86	    inference('lazy_cnf_exists', [status(thm)], ['718'])).
29.16/4.86	tff('720', plain,
29.16/4.86	    (![X0]: ~ cQ(X0))
29.16/4.86	      <= (~ ( (!!(cQ))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))))),
29.16/4.86	    inference('sup-', [status(thm)], ['717', '719'])).
29.16/4.86	tff('721', plain,
29.16/4.86	    ~ ( (??(cQ))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))) | 
29.16/4.86	    ( (!!(cQ))), inference('sup-', [status(thm)], ['716', '720'])).
29.16/4.86	tff('722', plain,
29.16/4.86	    ((!!(cQ)) = (??(cP))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))
29.16/4.86	      = ((!!(cQ)) <=> (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['27'])).
29.16/4.86	tff('723', plain, ~ ( (??(cQ))) | ( '#form13'),
29.16/4.86	    inference('split', [status(esa)], ['143'])).
29.16/4.86	tff('724', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS)))),
29.16/4.86	    inference('split', [status(esa)], ['150'])).
29.16/4.86	tff('725', plain, (![X1]:  cR(X1)) <= (( (!!(cR)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['657'])).
29.16/4.86	tff('726', plain,
29.16/4.86	    (![X1]: cR('#sk4'(X1)) != cR(X1))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['499'])).
29.16/4.86	tff('727', plain,
29.16/4.86	    (![X0]: ~ cR(X0))
29.16/4.86	      <= (~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))) & 
29.16/4.86	          ( (!!(cR)))),
29.16/4.86	    inference('sup-', [status(thm)], ['725', '726'])).
29.16/4.86	tff('728', plain, (![X1]:  cR(X1)) <= (( (!!(cR)))),
29.16/4.86	    inference('lazy_cnf_forall', [status(thm)], ['657'])).
29.16/4.86	tff('729', plain,
29.16/4.86	    ~ ( (!!(cR))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))),
29.16/4.86	    inference('demod', [status(thm)], ['727', '728'])).
29.16/4.86	tff('730', plain,
29.16/4.86	    ~
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.16/4.86	    ~
29.16/4.86	    (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	      ((!!(cQ)) <=> (??(cP))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0)))))))) <=>
29.16/4.86	         ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('split', [status(esa)], ['3'])).
29.16/4.86	tff('731', plain,
29.16/4.86	    ((??(cQ)) != (!!(cR)))
29.16/4.86	      <= (~
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['313'])).
29.16/4.86	tff('732', plain,
29.16/4.86	    (( (??(cQ)) |  (!!(cR))))
29.16/4.86	      <= (~
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) & 
29.16/4.86	          ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['731'])).
29.16/4.86	tff('733', plain,
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ( (!!(cR))) | 
29.16/4.86	    ~ ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ( (??(cQ))), inference('split', [status(esa)], ['732'])).
29.16/4.86	tff('734', plain,
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      <= ((((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('split', [status(esa)], ['150'])).
29.16/4.86	tff('735', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS)))))),
29.16/4.86	    inference('split', [status(esa)], ['132'])).
29.16/4.86	tff('736', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=> ((??(cQ)) <=> (!!(cR))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('sup+', [status(thm)], ['734', '735'])).
29.16/4.86	tff('737', plain,
29.16/4.86	    ( ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['736'])).
29.16/4.86	tff('738', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS))))
29.16/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['737'])).
29.16/4.86	tff('739', plain,
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	      = ((??(cR)) <=> (!!(cS))))
29.16/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['737'])).
29.16/4.86	tff('740', plain,
29.16/4.86	    (~ '#form27'
29.16/4.86	     |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    define([status(thm)])).
29.16/4.86	tff('741', plain,
29.16/4.86	    ( '#form27')
29.16/4.86	      <= (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	            (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	            = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	               ((??(cR)) <=> (!!(cS))))) & 
29.16/4.86	          (((??(cQ)) <=> (!!(cR)))
29.16/4.86	            = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))),
29.16/4.86	    inference('renaming', [status(thm)], ['738', '740'])).
29.16/4.86	tff('742', plain,
29.16/4.86	    (~ '#form27'
29.16/4.86	     |  ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))),
29.16/4.86	    define([status(thm)])).
29.16/4.86	tff('743', plain,
29.16/4.86	    (~ '#form27'
29.16/4.86	     | (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1))))))))
29.16/4.86	        = ((??(cR)) <=> (!!(cS)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['742'])).
29.16/4.86	tff('744', plain, (~ '#form27') <= (~ ( '#form27')),
29.16/4.86	    inference('split', [status(esa)], ['743'])).
29.16/4.86	tff('745', plain,
29.16/4.86	    ~
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.16/4.86	    ~
29.16/4.86	    (((??(cQ)) <=> (!!(cR)))
29.16/4.86	      = (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) | 
29.16/4.86	    ( '#form27'), inference('sup-', [status(thm)], ['741', '744'])).
29.16/4.86	tff('746', plain, ((!!(cQ)) = (??(cP))) <= (((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('split', [status(esa)], ['27'])).
29.16/4.86	tff('747', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	          ((!!(cQ)) <=> (??(cP)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS))))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['102'])).
29.16/4.86	tff('748', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))) <=>
29.16/4.86	          ((!!(cQ)) <=> (!!(cQ)))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('sup-', [status(thm)], ['746', '747'])).
29.16/4.86	tff('749', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	      ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	       ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      != (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1)))))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('simplify boolean subterms', [status(thm)], ['748'])).
29.16/4.86	tff('750', plain,
29.16/4.86	    (( ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	         (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1))))))))) <=>
29.16/4.86	        ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS)))))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('lazy_cnf_xor', [status(thm)], ['749'])).
29.16/4.86	tff('751', plain,
29.16/4.86	    (((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	       (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	       = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	          ((??(cR)) <=> (!!(cS))))
29.16/4.86	      |  (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))))
29.16/4.86	      <= (((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	            = ((!!(cP)) <=> (??(cS)))) & 
29.16/4.86	          ((!!(cQ)) = (??(cP)))),
29.16/4.86	    inference('simplify nested equalities', [status(thm)], ['750'])).
29.16/4.86	tff('752', plain,
29.16/4.86	    ((((??(cQ)) <=> (!!(cR))) <=>
29.16/4.86	      (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cP(Y0) <=> cP(Y1)))))))))
29.16/4.86	      = ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cQ(Y0) <=> cQ(Y1)))))))) <=>
29.16/4.86	         ((??(cR)) <=> (!!(cS))))) | 
29.16/4.86	    ~
29.16/4.86	    ((??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cR(Y1) <=> cR(Y0))))))))
29.16/4.86	      = ((!!(cP)) <=> (??(cS)))) | 
29.16/4.86	    ( (??((^[Y0 : $i]: (!!((^[Y1 : $i]: (cS(Y0) <=> cS(Y1))))))))) | 
29.16/4.86	    ~ ((!!(cQ)) = (??(cP))), inference('split', [status(esa)], ['751'])).
29.16/4.86	tff('753', plain, $false,
29.16/4.86	    inference('sat_resolution*', [status(thm)],
29.16/4.86	              ['12', '24', '33', '46', '52', '58', '71', '74', '83', '89', 
29.16/4.86	               '98', '108', '115', '129', '136', '158', '173', '186', '191', 
29.16/4.86	               '202', '206', '220', '224', '227', '237', '240', '241', 
29.16/4.86	               '251', '265', '272', '277', '289', '299', '300', '304', 
29.16/4.86	               '308', '318', '321', '335', '336', '337', '347', '354', 
29.16/4.86	               '364', '368', '373', '383', '387', '394', '405', '415', 
29.16/4.86	               '419', '423', '427', '438', '443', '447', '450', '451', 
29.16/4.86	               '452', '456', '459', '466', '470', '473', '482', '485', 
29.16/4.86	               '489', '496', '506', '512', '518', '519', '522', '525', 
29.16/4.86	               '528', '529', '534', '535', '538', '542', '543', '546', 
29.16/4.86	               '552', '564', '567', '568', '572', '573', '576', '579', 
29.16/4.86	               '584', '592', '595', '608', '609', '621', '624', '628', 
29.16/4.86	               '629', '632', '638', '641', '644', '648', '652', '655', 
29.16/4.86	               '656', '660', '666', '678', '686', '692', '693', '700', 
29.16/4.86	               '709', '715', '721', '722', '723', '724', '729', '730', 
29.16/4.86	               '733', '745', '752'])).
29.16/4.86	
29.16/4.86	% SZS output end Refutation
29.16/4.86	
29.16/4.86	
29.16/4.86	% Terminating...
29.45/4.96	% Runner terminated.
29.45/4.97	% Zipperpin 1.5 exiting
29.45/4.97	EOF