0.00/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.11	% Command    : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.tuwABSY6lN
0.10/0.31	% Computer   : n018.cluster.edu
0.10/0.31	% Model      : x86_64 x86_64
0.10/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory     : 8042.1875MB
0.10/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 960
0.10/0.31	% DateTime   : Thu Jul  2 08:44:37 EDT 2020
0.10/0.31	% CPUTime    : 
0.10/0.31	% Running portfolio for 120 s
0.10/0.31	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.10/0.32	% Number of cores: 8
0.10/0.32	% Python version: Python 3.6.8
0.16/0.32	% Running in FO mode
19.06/19.36	% Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25
19.06/19.36	% Solved by: fo/fo7.sh
19.06/19.36	To remain in the chosen logic fragment, unification with booleans has been disabled.
19.06/19.36	% done 25124 iterations in 18.923s
19.06/19.36	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
19.06/19.36	% SZS output start Refutation
19.06/19.36	tff(t_a_in_b, axiom,
19.06/19.36	  ((incident(a2,b3b1) & incident(a3,b1b2) & incident(a1,b2b3)) => goal)).
19.06/19.36	tff('0', plain,
19.06/19.36	    ( goal
19.06/19.36	     | ~ incident(a1, b2b3)
19.06/19.36	     | ~ incident(a3, b1b2)
19.06/19.36	     | ~ incident(a2, b3b1)),
19.06/19.36	    inference('cnf', [status(esa)], [t_a_in_b])).
19.06/19.36	tff('1', plain,
19.06/19.36	    ~ ( incident(a3, b1b2)) | ~ ( incident(a1, b2b3)) | ( goal) | 
19.06/19.36	    ~ ( incident(a2, b3b1)), inference('split', [status(esa)], ['0'])).
19.06/19.36	tff(gap3, axiom, (incident(b2,a3a1) | incident(a3,b1b2))).
19.06/19.36	tff('2', plain, ( incident(b2, a3a1) |  incident(a3, b1b2)),
19.06/19.36	    inference('cnf', [status(esa)], [gap3])).
19.06/19.36	tff('3', plain, ( incident(b2, a3a1)) <= (( incident(b2, a3a1))),
19.06/19.36	    inference('split', [status(esa)], ['2'])).
19.06/19.36	tff(ib2b3, axiom, (incident(b2,b2b3))).
19.06/19.36	tff('4', plain,  incident(b2, b2b3), inference('cnf', [status(esa)], [ib2b3])).
19.06/19.36	tff(ia1a3, axiom, (incident(a1,a3a1))).
19.06/19.36	tff('5', plain,  incident(a1, a3a1), inference('cnf', [status(esa)], [ia1a3])).
19.06/19.36	tff(gap1, axiom, (incident(b3,a1a2) | incident(a1,b2b3))).
19.06/19.36	tff('6', plain, ( incident(b3, a1a2) |  incident(a1, b2b3)),
19.06/19.36	    inference('cnf', [status(esa)], [gap1])).
19.06/19.36	tff('7', plain, ( incident(a1, b2b3)) <= (( incident(a1, b2b3))),
19.06/19.36	    inference('split', [status(esa)], ['6'])).
19.06/19.36	tff(unique, axiom,
19.06/19.36	  (![A,B,C,D]:
19.06/19.36	     ((incident(A,C) & incident(A,D) & incident(B,C) & incident(B,D)) =>
19.06/19.36	      ((C = D) | (B = A))))).
19.06/19.36	tff('8', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('9', plain,
19.06/19.36	    (![X0, X1]:
19.06/19.36	       (b2b3 = X0
19.06/19.36	        | ~ incident(a1, X0)
19.06/19.36	        | ~ incident(X1, X0)
19.06/19.36	        | ~ incident(X1, b2b3)
19.06/19.36	        | a1 = X1))
19.06/19.36	      <= (( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['7', '8'])).
19.06/19.36	tff('10', plain,
19.06/19.36	    (![X0]:
19.06/19.36	       (a1 = X0 | ~ incident(X0, b2b3) | ~ incident(X0, a3a1) | b2b3 = a3a1))
19.06/19.36	      <= (( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['5', '9'])).
19.06/19.36	tff('11', plain,
19.06/19.36	    ((b2b3 = a3a1 | ~ incident(b2, a3a1) | a1 = b2))
19.06/19.36	      <= (( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['4', '10'])).
19.06/19.36	tff('12', plain,
19.06/19.36	    ((a1 = b2 | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['3', '11'])).
19.06/19.36	tff(ib2b1, axiom, (incident(b2,b1b2))).
19.06/19.36	tff('13', plain,  incident(b2, b1b2),
19.06/19.36	    inference('cnf', [status(esa)], [ib2b1])).
19.06/19.36	tff('14', plain,
19.06/19.36	    (( incident(a1, b1b2) | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['12', '13'])).
19.06/19.36	tff(ia1s1, axiom, (incident(a1,s1))).
19.06/19.36	tff('15', plain,  incident(a1, s1), inference('cnf', [status(esa)], [ia1s1])).
19.06/19.36	tff(ib1b2, axiom, (incident(b1,b1b2))).
19.06/19.36	tff('16', plain,  incident(b1, b1b2),
19.06/19.36	    inference('cnf', [status(esa)], [ib1b2])).
19.06/19.36	tff(ib1s1, axiom, (incident(b1,s1))).
19.06/19.36	tff('17', plain,  incident(b1, s1), inference('cnf', [status(esa)], [ib1s1])).
19.06/19.36	tff('18', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('19', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (s1 = X0
19.06/19.36	       | ~ incident(b1, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, s1)
19.06/19.36	       | b1 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['17', '18'])).
19.06/19.36	tff('20', plain,
19.06/19.36	    ![X0]: (b1 = X0 | ~ incident(X0, s1) | ~ incident(X0, b1b2) | s1 = b1b2),
19.06/19.36	    inference('sup-', [status(thm)], ['16', '19'])).
19.06/19.36	tff('21', plain, (s1 = b1b2 | ~ incident(a1, b1b2) | b1 = a1),
19.06/19.36	    inference('sup-', [status(thm)], ['15', '20'])).
19.06/19.36	tff('22', plain,
19.06/19.36	    ((b2b3 = a3a1 | b1 = a1 | s1 = b1b2))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['14', '21'])).
19.06/19.36	tff('23', plain,
19.06/19.36	    ((a1 = b2 | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['3', '11'])).
19.06/19.36	tff(diff_b1_b2, axiom, ((b1 = b2) => goal)).
19.06/19.36	tff('24', plain, ( goal | b1 != b2),
19.06/19.36	    inference('cnf', [status(esa)], [diff_b1_b2])).
19.06/19.36	tff('25', plain, (b1 != b2) <= (~ (b1 = b2)),
19.06/19.36	    inference('split', [status(esa)], ['24'])).
19.06/19.36	tff(diff_a3_a1, axiom, ((a1 = a3) => goal)).
19.06/19.36	tff('26', plain, ( goal | a1 != a3),
19.06/19.36	    inference('cnf', [status(esa)], [diff_a3_a1])).
19.06/19.36	tff('27', plain, ( goal) <= (( goal)),
19.06/19.36	    inference('split', [status(esa)], ['26'])).
19.06/19.36	tff(goal_to_be_proved, conjecture, (goal)).
19.06/19.36	tff(zf_stmt_0, negated_conjecture, (~goal)).
19.06/19.36	tff('28', plain, ~ goal, inference('cnf', [status(esa)], [zf_stmt_0])).
19.06/19.36	tff('29', plain, ~ ( goal), inference('sup-', [status(thm)], ['27', '28'])).
19.06/19.36	tff('30', plain, ~ (b1 = b2) | ( goal),
19.06/19.36	    inference('split', [status(esa)], ['24'])).
19.06/19.36	tff('31', plain, ~ (b1 = b2),
19.06/19.36	    inference('sat_resolution*', [status(thm)], ['29', '30'])).
19.06/19.36	tff('32', plain, b1 != b2,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['25', '31'])).
19.06/19.36	tff('33', plain,
19.06/19.36	    ((b1 != a1 | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['23', '32'])).
19.06/19.36	tff('34', plain,
19.06/19.36	    ((s1 = b1b2 | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('clc', [status(thm)], ['22', '33'])).
19.06/19.36	tff('35', plain,
19.06/19.36	    ((a1 = b2 | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['3', '11'])).
19.06/19.36	tff(ib2s2, axiom, (incident(b2,s2))).
19.06/19.36	tff('36', plain,  incident(b2, s2), inference('cnf', [status(esa)], [ib2s2])).
19.06/19.36	tff('37', plain,
19.06/19.36	    (( incident(a1, s2) | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['35', '36'])).
19.06/19.36	tff(iss1, axiom, (incident(s,s1))).
19.06/19.36	tff('38', plain,  incident(s, s1), inference('cnf', [status(esa)], [iss1])).
19.06/19.36	tff(iss2, axiom, (incident(s,s2))).
19.06/19.36	tff('39', plain,  incident(s, s2), inference('cnf', [status(esa)], [iss2])).
19.06/19.36	tff('40', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('41', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (s2 = X0
19.06/19.36	       | ~ incident(s, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, s2)
19.06/19.36	       | s = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['39', '40'])).
19.06/19.36	tff('42', plain,
19.06/19.36	    ![X0]: (s = X0 | ~ incident(X0, s2) | ~ incident(X0, s1) | s2 = s1),
19.06/19.36	    inference('sup-', [status(thm)], ['38', '41'])).
19.06/19.36	tff('43', plain,
19.06/19.36	    ((b2b3 = a3a1 | s2 = s1 | ~ incident(a1, s1) | s = a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['37', '42'])).
19.06/19.36	tff('44', plain,  incident(a1, s1), inference('cnf', [status(esa)], [ia1s1])).
19.06/19.36	tff('45', plain,
19.06/19.36	    ((b2b3 = a3a1 | s2 = s1 | s = a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['43', '44'])).
19.06/19.36	tff(ia2a1, axiom, (incident(a2,a1a2))).
19.06/19.36	tff('46', plain,  incident(a2, a1a2),
19.06/19.36	    inference('cnf', [status(esa)], [ia2a1])).
19.06/19.36	tff('47', plain,  incident(a1, s1), inference('cnf', [status(esa)], [ia1s1])).
19.06/19.36	tff(ia1a2, axiom, (incident(a1,a1a2))).
19.06/19.36	tff('48', plain,  incident(a1, a1a2),
19.06/19.36	    inference('cnf', [status(esa)], [ia1a2])).
19.06/19.36	tff('49', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('50', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (a1a2 = X0
19.06/19.36	       | ~ incident(a1, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, a1a2)
19.06/19.36	       | a1 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['48', '49'])).
19.06/19.36	tff('51', plain,
19.06/19.36	    ![X0]: (a1 = X0 | ~ incident(X0, a1a2) | ~ incident(X0, s1) | a1a2 = s1),
19.06/19.36	    inference('sup-', [status(thm)], ['47', '50'])).
19.06/19.36	tff('52', plain, (a1a2 = s1 | ~ incident(a2, s1) | a1 = a2),
19.06/19.36	    inference('sup-', [status(thm)], ['46', '51'])).
19.06/19.36	tff(diff_a1_a2, axiom, ((a2 = a1) => goal)).
19.06/19.36	tff('53', plain, ( goal | a2 != a1),
19.06/19.36	    inference('cnf', [status(esa)], [diff_a1_a2])).
19.06/19.36	tff('54', plain, (a2 != a1) <= (~ (a2 = a1)),
19.06/19.36	    inference('split', [status(esa)], ['53'])).
19.06/19.36	tff('55', plain, ~ (a2 = a1) | ( goal),
19.06/19.36	    inference('split', [status(esa)], ['53'])).
19.06/19.36	tff('56', plain, ~ (a2 = a1),
19.06/19.36	    inference('sat_resolution*', [status(thm)], ['29', '55'])).
19.06/19.36	tff('57', plain, a2 != a1,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['54', '56'])).
19.06/19.36	tff('58', plain, (a1a2 = s1 | ~ incident(a2, s1)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['52', '57'])).
19.06/19.36	tff('59', plain,
19.06/19.36	    ((~ incident(a2, s2) | s = a1 | b2b3 = a3a1 | a1a2 = s1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['45', '58'])).
19.06/19.36	tff(ia2s2, axiom, (incident(a2,s2))).
19.06/19.36	tff('60', plain,  incident(a2, s2), inference('cnf', [status(esa)], [ia2s2])).
19.06/19.36	tff('61', plain,
19.06/19.36	    ((s = a1 | b2b3 = a3a1 | a1a2 = s1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['59', '60'])).
19.06/19.36	tff('62', plain,
19.06/19.36	    ((a1a2 = b1b2 | b2b3 = a3a1 | b2b3 = a3a1 | s = a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['34', '61'])).
19.06/19.36	tff('63', plain,
19.06/19.36	    ((s = a1 | b2b3 = a3a1 | a1a2 = b1b2))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('simplify', [status(thm)], ['62'])).
19.06/19.36	tff(not12, axiom, ((a1a2 = b1b2) => goal)).
19.06/19.36	tff('64', plain, ( goal | a1a2 != b1b2),
19.06/19.36	    inference('cnf', [status(esa)], [not12])).
19.06/19.36	tff('65', plain, (a1a2 != b1b2) <= (~ (a1a2 = b1b2)),
19.06/19.36	    inference('split', [status(esa)], ['64'])).
19.06/19.36	tff('66', plain, ~ (a1a2 = b1b2) | ( goal),
19.06/19.36	    inference('split', [status(esa)], ['64'])).
19.06/19.36	tff('67', plain, ~ (a1a2 = b1b2),
19.06/19.36	    inference('sat_resolution*', [status(thm)], ['29', '66'])).
19.06/19.36	tff('68', plain, a1a2 != b1b2,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['65', '67'])).
19.06/19.36	tff('69', plain,
19.06/19.36	    ((s = a1 | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['63', '68'])).
19.06/19.36	tff(iss3, axiom, (incident(s,s3))).
19.06/19.36	tff('70', plain,  incident(s, s3), inference('cnf', [status(esa)], [iss3])).
19.06/19.36	tff('71', plain,
19.06/19.36	    (( incident(a1, s3) | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['69', '70'])).
19.06/19.36	tff('72', plain,  incident(a1, a3a1),
19.06/19.36	    inference('cnf', [status(esa)], [ia1a3])).
19.06/19.36	tff(ia3s3, axiom, (incident(a3,s3))).
19.06/19.36	tff('73', plain,  incident(a3, s3), inference('cnf', [status(esa)], [ia3s3])).
19.06/19.36	tff(ia3a1, axiom, (incident(a3,a3a1))).
19.06/19.36	tff('74', plain,  incident(a3, a3a1),
19.06/19.36	    inference('cnf', [status(esa)], [ia3a1])).
19.06/19.36	tff('75', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('76', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (a3a1 = X0
19.06/19.36	       | ~ incident(a3, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, a3a1)
19.06/19.36	       | a3 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['74', '75'])).
19.06/19.36	tff('77', plain,
19.06/19.36	    ![X0]: (a3 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, s3) | a3a1 = s3),
19.06/19.36	    inference('sup-', [status(thm)], ['73', '76'])).
19.06/19.36	tff('78', plain, (a3a1 = s3 | ~ incident(a1, s3) | a3 = a1),
19.06/19.36	    inference('sup-', [status(thm)], ['72', '77'])).
19.06/19.36	tff('79', plain, ( goal | a1 != a3),
19.06/19.36	    inference('cnf', [status(esa)], [diff_a3_a1])).
19.06/19.36	tff('80', plain, ~ goal, inference('cnf', [status(esa)], [zf_stmt_0])).
19.06/19.36	tff('81', plain, a1 != a3, inference('clc', [status(thm)], ['79', '80'])).
19.06/19.36	tff('82', plain, (a3a1 = s3 | ~ incident(a1, s3)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['78', '81'])).
19.06/19.36	tff('83', plain,
19.06/19.36	    ((b2b3 = a3a1 | a3a1 = s3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['71', '82'])).
19.06/19.36	tff('84', plain,
19.06/19.36	    (( incident(a1, s3) | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['69', '70'])).
19.06/19.36	tff('85', plain,
19.06/19.36	    ((a1 = b2 | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['3', '11'])).
19.06/19.36	tff('86', plain,  incident(b2, b2b3),
19.06/19.36	    inference('cnf', [status(esa)], [ib2b3])).
19.06/19.36	tff(ib3s3, axiom, (incident(b3,s3))).
19.06/19.36	tff('87', plain,  incident(b3, s3), inference('cnf', [status(esa)], [ib3s3])).
19.06/19.36	tff(ib3b2, axiom, (incident(b3,b2b3))).
19.06/19.36	tff('88', plain,  incident(b3, b2b3),
19.06/19.36	    inference('cnf', [status(esa)], [ib3b2])).
19.06/19.36	tff('89', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('90', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (b2b3 = X0
19.06/19.36	       | ~ incident(b3, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, b2b3)
19.06/19.36	       | b3 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['88', '89'])).
19.06/19.36	tff('91', plain,
19.06/19.36	    ![X0]: (b3 = X0 | ~ incident(X0, b2b3) | ~ incident(X0, s3) | b2b3 = s3),
19.06/19.36	    inference('sup-', [status(thm)], ['87', '90'])).
19.06/19.36	tff('92', plain, (b2b3 = s3 | ~ incident(b2, s3) | b3 = b2),
19.06/19.36	    inference('sup-', [status(thm)], ['86', '91'])).
19.06/19.36	tff(diff_b2_b3, axiom, ((b3 = b2) => goal)).
19.06/19.36	tff('93', plain, ( goal | b3 != b2),
19.06/19.36	    inference('cnf', [status(esa)], [diff_b2_b3])).
19.06/19.36	tff('94', plain, (b3 != b2) <= (~ (b3 = b2)),
19.06/19.36	    inference('split', [status(esa)], ['93'])).
19.06/19.36	tff('95', plain, ~ (b3 = b2) | ( goal),
19.06/19.36	    inference('split', [status(esa)], ['93'])).
19.06/19.36	tff('96', plain, ~ (b3 = b2),
19.06/19.36	    inference('sat_resolution*', [status(thm)], ['29', '95'])).
19.06/19.36	tff('97', plain, b3 != b2,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['94', '96'])).
19.06/19.36	tff('98', plain, (b2b3 = s3 | ~ incident(b2, s3)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['92', '97'])).
19.06/19.36	tff('99', plain,
19.06/19.36	    ((~ incident(a1, s3) | b2b3 = a3a1 | b2b3 = s3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['85', '98'])).
19.06/19.36	tff('100', plain,
19.06/19.36	    ((b2b3 = a3a1 | b2b3 = s3 | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['84', '99'])).
19.06/19.36	tff('101', plain,
19.06/19.36	    ((b2b3 = s3 | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('simplify', [status(thm)], ['100'])).
19.06/19.36	tff('102', plain,
19.06/19.36	    ((b2b3 = a3a1 | b2b3 = a3a1 | b2b3 = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['83', '101'])).
19.06/19.36	tff('103', plain,
19.06/19.36	    (b2b3 = a3a1) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('simplify', [status(thm)], ['102'])).
19.06/19.36	tff('104', plain,  incident(b3, b2b3),
19.06/19.36	    inference('cnf', [status(esa)], [ib3b2])).
19.06/19.36	tff('105', plain,
19.06/19.36	    ( incident(b3, a3a1)) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['103', '104'])).
19.06/19.36	tff('106', plain,
19.06/19.36	    ![X0]: (a3 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, s3) | a3a1 = s3),
19.06/19.36	    inference('sup-', [status(thm)], ['73', '76'])).
19.06/19.36	tff('107', plain,
19.06/19.36	    ((a3a1 = s3 | ~ incident(b3, s3) | a3 = b3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['105', '106'])).
19.06/19.36	tff('108', plain,  incident(b3, s3), inference('cnf', [status(esa)], [ib3s3])).
19.06/19.36	tff('109', plain,
19.06/19.36	    ((a3a1 = s3 | a3 = b3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['107', '108'])).
19.06/19.36	tff('110', plain,  incident(s, s3), inference('cnf', [status(esa)], [iss3])).
19.06/19.36	tff('111', plain,
19.06/19.36	    (( incident(s, a3a1) | a3 = b3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['109', '110'])).
19.06/19.36	tff('112', plain,  incident(a1, s1), inference('cnf', [status(esa)], [ia1s1])).
19.06/19.36	tff('113', plain,  incident(a1, a3a1),
19.06/19.36	    inference('cnf', [status(esa)], [ia1a3])).
19.06/19.36	tff('114', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('115', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (a3a1 = X0
19.06/19.36	       | ~ incident(a1, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, a3a1)
19.06/19.36	       | a1 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['113', '114'])).
19.06/19.36	tff('116', plain,
19.06/19.36	    ![X0]: (a1 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, s1) | a3a1 = s1),
19.06/19.36	    inference('sup-', [status(thm)], ['112', '115'])).
19.06/19.36	tff('117', plain,
19.06/19.36	    ((a3 = b3 | a3a1 = s1 | ~ incident(s, s1) | a1 = s))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['111', '116'])).
19.06/19.36	tff('118', plain,  incident(s, s1), inference('cnf', [status(esa)], [iss1])).
19.06/19.36	tff('119', plain,
19.06/19.36	    ((a3 = b3 | a3a1 = s1 | a1 = s))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['117', '118'])).
19.06/19.36	tff('120', plain,  incident(b1, s1), inference('cnf', [status(esa)], [ib1s1])).
19.06/19.36	tff('121', plain,
19.06/19.36	    (( incident(b1, a3a1) | a1 = s | a3 = b3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['119', '120'])).
19.06/19.36	tff(ip2b, axiom, (incident(p2,b3b1))).
19.06/19.36	tff('122', plain,  incident(p2, b3b1),
19.06/19.36	    inference('cnf', [status(esa)], [ip2b])).
19.06/19.36	tff(ip2a, axiom, (incident(p2,a3a1))).
19.06/19.36	tff('123', plain,  incident(p2, a3a1),
19.06/19.36	    inference('cnf', [status(esa)], [ip2a])).
19.06/19.36	tff('124', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('125', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (a3a1 = X0
19.06/19.36	       | ~ incident(p2, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, a3a1)
19.06/19.36	       | p2 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['123', '124'])).
19.06/19.36	tff('126', plain,
19.06/19.36	    ![X0]:
19.06/19.36	      (p2 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, b3b1) | a3a1 = b3b1),
19.06/19.36	    inference('sup-', [status(thm)], ['122', '125'])).
19.06/19.36	tff(not31, axiom, ((b3b1 = a3a1) => goal)).
19.06/19.36	tff('127', plain, ( goal | b3b1 != a3a1),
19.06/19.36	    inference('cnf', [status(esa)], [not31])).
19.06/19.36	tff('128', plain, (b3b1 != a3a1) <= (~ (b3b1 = a3a1)),
19.06/19.36	    inference('split', [status(esa)], ['127'])).
19.06/19.36	tff('129', plain, ~ (b3b1 = a3a1) | ( goal),
19.06/19.36	    inference('split', [status(esa)], ['127'])).
19.06/19.36	tff('130', plain, ~ (b3b1 = a3a1),
19.06/19.36	    inference('sat_resolution*', [status(thm)], ['29', '129'])).
19.06/19.36	tff('131', plain, b3b1 != a3a1,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['128', '130'])).
19.06/19.36	tff('132', plain,
19.06/19.36	    ![X0]: (p2 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, b3b1)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['126', '131'])).
19.06/19.36	tff('133', plain,
19.06/19.36	    ((a3 = b3 | a1 = s | ~ incident(b1, b3b1) | p2 = b1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['121', '132'])).
19.06/19.36	tff(ib1b3, axiom, (incident(b1,b3b1))).
19.06/19.36	tff('134', plain,  incident(b1, b3b1),
19.06/19.36	    inference('cnf', [status(esa)], [ib1b3])).
19.06/19.36	tff('135', plain,
19.06/19.36	    ( incident(b3, a3a1)) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['103', '104'])).
19.06/19.36	tff('136', plain,
19.06/19.36	    ![X0]: (p2 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, b3b1)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['126', '131'])).
19.06/19.36	tff('137', plain,
19.06/19.36	    ((~ incident(b3, b3b1) | p2 = b3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['135', '136'])).
19.06/19.36	tff(ib3b1, axiom, (incident(b3,b3b1))).
19.06/19.36	tff('138', plain,  incident(b3, b3b1),
19.06/19.36	    inference('cnf', [status(esa)], [ib3b1])).
19.06/19.36	tff('139', plain,
19.06/19.36	    (p2 = b3) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['137', '138'])).
19.06/19.36	tff('140', plain,
19.06/19.36	    ((a3 = b3 | a1 = s | b3 = b1))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['133', '134', '139'])).
19.06/19.36	tff(diff_b3_b1, axiom, ((b1 = b3) => goal)).
19.06/19.36	tff('141', plain, ( goal | b1 != b3),
19.06/19.36	    inference('cnf', [status(esa)], [diff_b3_b1])).
19.06/19.36	tff('142', plain, ~ goal, inference('cnf', [status(esa)], [zf_stmt_0])).
19.06/19.36	tff('143', plain, b1 != b3, inference('clc', [status(thm)], ['141', '142'])).
19.06/19.36	tff('144', plain,
19.06/19.36	    ((a3 = b3 | a1 = s)) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['140', '143'])).
19.06/19.36	tff('145', plain,  incident(s, s2), inference('cnf', [status(esa)], [iss2])).
19.06/19.36	tff('146', plain,
19.06/19.36	    (( incident(a1, s2) | a3 = b3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['144', '145'])).
19.06/19.36	tff('147', plain,  incident(a1, a1a2),
19.06/19.36	    inference('cnf', [status(esa)], [ia1a2])).
19.06/19.36	tff('148', plain,  incident(a2, s2), inference('cnf', [status(esa)], [ia2s2])).
19.06/19.36	tff('149', plain,  incident(a2, a1a2),
19.06/19.36	    inference('cnf', [status(esa)], [ia2a1])).
19.06/19.36	tff('150', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('151', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (a1a2 = X0
19.06/19.36	       | ~ incident(a2, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, a1a2)
19.06/19.36	       | a2 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['149', '150'])).
19.06/19.36	tff('152', plain,
19.06/19.36	    ![X0]: (a2 = X0 | ~ incident(X0, a1a2) | ~ incident(X0, s2) | a1a2 = s2),
19.06/19.36	    inference('sup-', [status(thm)], ['148', '151'])).
19.06/19.36	tff('153', plain, (a1a2 = s2 | ~ incident(a1, s2) | a2 = a1),
19.06/19.36	    inference('sup-', [status(thm)], ['147', '152'])).
19.06/19.36	tff('154', plain, a2 != a1,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['54', '56'])).
19.06/19.36	tff('155', plain, (a1a2 = s2 | ~ incident(a1, s2)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['153', '154'])).
19.06/19.36	tff('156', plain,
19.06/19.36	    ((a3 = b3 | a1a2 = s2))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['146', '155'])).
19.06/19.36	tff('157', plain,  incident(b2, s2), inference('cnf', [status(esa)], [ib2s2])).
19.06/19.36	tff('158', plain,
19.06/19.36	    (( incident(b2, a1a2) | a3 = b3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['156', '157'])).
19.06/19.36	tff(ip3b, axiom, (incident(p3,b1b2))).
19.06/19.36	tff('159', plain,  incident(p3, b1b2),
19.06/19.36	    inference('cnf', [status(esa)], [ip3b])).
19.06/19.36	tff(ip3a, axiom, (incident(p3,a1a2))).
19.06/19.36	tff('160', plain,  incident(p3, a1a2),
19.06/19.36	    inference('cnf', [status(esa)], [ip3a])).
19.06/19.36	tff('161', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('162', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (a1a2 = X0
19.06/19.36	       | ~ incident(p3, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, a1a2)
19.06/19.36	       | p3 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['160', '161'])).
19.06/19.36	tff('163', plain,
19.06/19.36	    ![X0]:
19.06/19.36	      (p3 = X0 | ~ incident(X0, a1a2) | ~ incident(X0, b1b2) | a1a2 = b1b2),
19.06/19.36	    inference('sup-', [status(thm)], ['159', '162'])).
19.06/19.36	tff('164', plain, a1a2 != b1b2,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['65', '67'])).
19.06/19.36	tff('165', plain,
19.06/19.36	    ![X0]: (p3 = X0 | ~ incident(X0, a1a2) | ~ incident(X0, b1b2)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['163', '164'])).
19.06/19.36	tff('166', plain,
19.06/19.36	    ((a3 = b3 | ~ incident(b2, b1b2) | p3 = b2))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['158', '165'])).
19.06/19.36	tff('167', plain,  incident(b2, b1b2),
19.06/19.36	    inference('cnf', [status(esa)], [ib2b1])).
19.06/19.36	tff('168', plain,
19.06/19.36	    ((a3 = b3 | p3 = b2)) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['166', '167'])).
19.06/19.36	tff(join, axiom,
19.06/19.36	  (![A,B]: ((point(A) & point(B)) => (?[C]: (incident(A,C) & incident(B,C)))))).
19.06/19.36	tff('169', plain,
19.06/19.36	    ![X16, X17]:
19.06/19.36	      (~ point(X16) | ~ point(X17) |  incident(X16, sk_C_1(X17, X16))),
19.06/19.36	    inference('cnf', [status(esa)], [join])).
19.06/19.36	tff('170', plain,
19.06/19.36	    ![X16, X17]:
19.06/19.36	      (~ point(X16) | ~ point(X17) |  incident(X17, sk_C_1(X17, X16))),
19.06/19.36	    inference('cnf', [status(esa)], [join])).
19.06/19.36	tff(goal_normal, axiom,
19.06/19.36	  (![A]: ((incident(p3,A) & incident(p1,A) & incident(p2,A)) => goal))).
19.06/19.36	tff('171', plain,
19.06/19.36	    ![X5]:
19.06/19.36	      ( goal | ~ incident(p3, X5) | ~ incident(p1, X5) | ~ incident(p2, X5)),
19.06/19.36	    inference('cnf', [status(esa)], [goal_normal])).
19.06/19.36	tff('172', plain,
19.06/19.36	    (![X5]: (~ incident(p3, X5) | ~ incident(p1, X5) | ~ incident(p2, X5)))
19.06/19.36	      <= ((![X5]:
19.06/19.36	             (~ incident(p3, X5) | ~ incident(p1, X5) | ~ incident(p2, X5)))),
19.06/19.36	    inference('split', [status(esa)], ['171'])).
19.06/19.36	tff('173', plain,
19.06/19.36	    (![X5]: (~ incident(p3, X5) | ~ incident(p1, X5) | ~ incident(p2, X5))) | 
19.06/19.36	    ( goal), inference('split', [status(esa)], ['171'])).
19.06/19.36	tff('174', plain,
19.06/19.36	    (![X5]: (~ incident(p3, X5) | ~ incident(p1, X5) | ~ incident(p2, X5))),
19.06/19.36	    inference('sat_resolution*', [status(thm)], ['29', '173'])).
19.06/19.36	tff('175', plain,
19.06/19.36	    ![X5]: (~ incident(p3, X5) | ~ incident(p1, X5) | ~ incident(p2, X5)),
19.06/19.36	    inference('simpl_trail', [status(thm)], ['172', '174'])).
19.06/19.36	tff('176', plain,
19.06/19.36	    ![X0]:
19.06/19.36	      (~ point(p3)
19.06/19.36	       | ~ point(X0)
19.06/19.36	       | ~ incident(p2, sk_C_1(p3, X0))
19.06/19.36	       | ~ incident(p1, sk_C_1(p3, X0))),
19.06/19.36	    inference('sup-', [status(thm)], ['170', '175'])).
19.06/19.36	tff('177', plain,  incident(p3, a1a2),
19.06/19.36	    inference('cnf', [status(esa)], [ip3a])).
19.06/19.36	tff(sort_point, axiom, (![A,B]: (incident(A,B) => point(A)))).
19.06/19.36	tff('178', plain, ![X11, X12]: ( point(X11) | ~ incident(X11, X12)),
19.06/19.36	    inference('cnf', [status(esa)], [sort_point])).
19.06/19.36	tff('179', plain,  point(p3),
19.06/19.36	    inference('sup-', [status(thm)], ['177', '178'])).
19.06/19.36	tff('180', plain,
19.06/19.36	    ![X0]:
19.06/19.36	      (~ point(X0)
19.06/19.36	       | ~ incident(p2, sk_C_1(p3, X0))
19.06/19.36	       | ~ incident(p1, sk_C_1(p3, X0))),
19.06/19.36	    inference('demod', [status(thm)], ['176', '179'])).
19.06/19.36	tff('181', plain,
19.06/19.36	    (~ point(p3) | ~ point(p2) | ~ incident(p1, sk_C_1(p3, p2)) | ~ point(p2)),
19.06/19.36	    inference('sup-', [status(thm)], ['169', '180'])).
19.06/19.36	tff('182', plain,  point(p3),
19.06/19.36	    inference('sup-', [status(thm)], ['177', '178'])).
19.06/19.36	tff('183', plain,  incident(p2, a3a1),
19.06/19.36	    inference('cnf', [status(esa)], [ip2a])).
19.06/19.36	tff('184', plain, ![X11, X12]: ( point(X11) | ~ incident(X11, X12)),
19.06/19.36	    inference('cnf', [status(esa)], [sort_point])).
19.06/19.36	tff('185', plain,  point(p2),
19.06/19.36	    inference('sup-', [status(thm)], ['183', '184'])).
19.06/19.36	tff('186', plain,  point(p2),
19.06/19.36	    inference('sup-', [status(thm)], ['183', '184'])).
19.06/19.36	tff('187', plain, ~ incident(p1, sk_C_1(p3, p2)),
19.06/19.36	    inference('demod', [status(thm)], ['181', '182', '185', '186'])).
19.06/19.36	tff('188', plain,
19.06/19.36	    ((~ incident(p1, sk_C_1(b2, p2)) | a3 = b3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['168', '187'])).
19.06/19.36	tff('189', plain,  incident(a3, a3a1),
19.06/19.36	    inference('cnf', [status(esa)], [ia3a1])).
19.06/19.36	tff('190', plain,
19.06/19.36	    (b2b3 = a3a1) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('simplify', [status(thm)], ['102'])).
19.06/19.36	tff(ip1a, axiom, (incident(p1,a2a3))).
19.06/19.36	tff('191', plain,  incident(p1, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ip1a])).
19.06/19.36	tff(ip1b, axiom, (incident(p1,b2b3))).
19.06/19.36	tff('192', plain,  incident(p1, b2b3),
19.06/19.36	    inference('cnf', [status(esa)], [ip1b])).
19.06/19.36	tff('193', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('194', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (b2b3 = X0
19.06/19.36	       | ~ incident(p1, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, b2b3)
19.06/19.36	       | p1 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['192', '193'])).
19.06/19.36	tff('195', plain,
19.06/19.36	    ![X0]:
19.06/19.36	      (p1 = X0 | ~ incident(X0, b2b3) | ~ incident(X0, a2a3) | b2b3 = a2a3),
19.06/19.36	    inference('sup-', [status(thm)], ['191', '194'])).
19.06/19.36	tff(not23, axiom, ((a2a3 = b2b3) => goal)).
19.06/19.36	tff('196', plain, ( goal | a2a3 != b2b3),
19.06/19.36	    inference('cnf', [status(esa)], [not23])).
19.06/19.36	tff('197', plain, (a2a3 != b2b3) <= (~ (a2a3 = b2b3)),
19.06/19.36	    inference('split', [status(esa)], ['196'])).
19.06/19.36	tff('198', plain, ~ (a2a3 = b2b3) | ( goal),
19.06/19.36	    inference('split', [status(esa)], ['196'])).
19.06/19.36	tff('199', plain, ~ (a2a3 = b2b3),
19.06/19.36	    inference('sat_resolution*', [status(thm)], ['29', '198'])).
19.06/19.36	tff('200', plain, a2a3 != b2b3,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['197', '199'])).
19.06/19.36	tff('201', plain,
19.06/19.36	    ![X0]: (p1 = X0 | ~ incident(X0, b2b3) | ~ incident(X0, a2a3)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['195', '200'])).
19.06/19.36	tff('202', plain,
19.06/19.36	    (![X0]: (~ incident(X0, a3a1) | ~ incident(X0, a2a3) | p1 = X0))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['190', '201'])).
19.06/19.36	tff('203', plain,
19.06/19.36	    ((p1 = a3 | ~ incident(a3, a2a3)))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['189', '202'])).
19.06/19.36	tff(ia3a2, axiom, (incident(a3,a2a3))).
19.06/19.36	tff('204', plain,  incident(a3, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ia3a2])).
19.06/19.36	tff('205', plain,
19.06/19.36	    (p1 = a3) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['203', '204'])).
19.06/19.36	tff('206', plain,
19.06/19.36	    (p2 = b3) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['137', '138'])).
19.06/19.36	tff('207', plain,
19.06/19.36	    (p2 = b3) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['137', '138'])).
19.06/19.36	tff('208', plain,  incident(p2, a3a1),
19.06/19.36	    inference('cnf', [status(esa)], [ip2a])).
19.06/19.36	tff('209', plain, ( incident(b2, a3a1)) <= (( incident(b2, a3a1))),
19.06/19.36	    inference('split', [status(esa)], ['2'])).
19.06/19.36	tff('210', plain,
19.06/19.36	    ![X16, X17]:
19.06/19.36	      (~ point(X16) | ~ point(X17) |  incident(X16, sk_C_1(X17, X16))),
19.06/19.36	    inference('cnf', [status(esa)], [join])).
19.06/19.36	tff('211', plain,
19.06/19.36	    ![X16, X17]:
19.06/19.36	      (~ point(X16) | ~ point(X17) |  incident(X17, sk_C_1(X17, X16))),
19.06/19.36	    inference('cnf', [status(esa)], [join])).
19.06/19.36	tff('212', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('213', plain,
19.06/19.36	    ![X0, X1, X2, X3]:
19.06/19.36	      (~ point(X1)
19.06/19.36	       | ~ point(X0)
19.06/19.36	       | sk_C_1(X1, X0) = X2
19.06/19.36	       | ~ incident(X1, X2)
19.06/19.36	       | ~ incident(X3, X2)
19.06/19.36	       | ~ incident(X3, sk_C_1(X1, X0))
19.06/19.36	       | X1 = X3),
19.06/19.36	    inference('sup-', [status(thm)], ['211', '212'])).
19.06/19.36	tff('214', plain,
19.06/19.36	    ![X0, X1, X2]:
19.06/19.36	      (~ point(X1)
19.06/19.36	       | ~ point(X0)
19.06/19.36	       | X1 = X0
19.06/19.36	       | ~ incident(X0, X2)
19.06/19.36	       | ~ incident(X1, X2)
19.06/19.36	       | sk_C_1(X1, X0) = X2
19.06/19.36	       | ~ point(X0)
19.06/19.36	       | ~ point(X1)),
19.06/19.36	    inference('sup-', [status(thm)], ['210', '213'])).
19.06/19.36	tff('215', plain,
19.06/19.36	    ![X0, X1, X2]:
19.06/19.36	      (sk_C_1(X1, X0) = X2
19.06/19.36	       | ~ incident(X1, X2)
19.06/19.36	       | ~ incident(X0, X2)
19.06/19.36	       | X1 = X0
19.06/19.36	       | ~ point(X0)
19.06/19.36	       | ~ point(X1)),
19.06/19.36	    inference('simplify', [status(thm)], ['214'])).
19.06/19.36	tff('216', plain,
19.06/19.36	    (![X0]:
19.06/19.36	       (~ point(b2)
19.06/19.36	        | ~ point(X0)
19.06/19.36	        | b2 = X0
19.06/19.36	        | ~ incident(X0, a3a1)
19.06/19.36	        | sk_C_1(b2, X0) = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1))),
19.06/19.36	    inference('sup-', [status(thm)], ['209', '215'])).
19.06/19.36	tff('217', plain,  incident(b2, s2), inference('cnf', [status(esa)], [ib2s2])).
19.06/19.36	tff('218', plain, ![X11, X12]: ( point(X11) | ~ incident(X11, X12)),
19.06/19.36	    inference('cnf', [status(esa)], [sort_point])).
19.06/19.36	tff('219', plain,  point(b2),
19.06/19.36	    inference('sup-', [status(thm)], ['217', '218'])).
19.06/19.36	tff('220', plain,
19.06/19.36	    (![X0]:
19.06/19.36	       (~ point(X0) | b2 = X0 | ~ incident(X0, a3a1) | sk_C_1(b2, X0) = a3a1))
19.06/19.36	      <= (( incident(b2, a3a1))),
19.06/19.36	    inference('demod', [status(thm)], ['216', '219'])).
19.06/19.36	tff('221', plain,
19.06/19.36	    ((sk_C_1(b2, p2) = a3a1 | b2 = p2 | ~ point(p2)))
19.06/19.36	      <= (( incident(b2, a3a1))),
19.06/19.36	    inference('sup-', [status(thm)], ['208', '220'])).
19.06/19.36	tff('222', plain,  point(p2),
19.06/19.36	    inference('sup-', [status(thm)], ['183', '184'])).
19.06/19.36	tff('223', plain,
19.06/19.36	    ((sk_C_1(b2, p2) = a3a1 | b2 = p2)) <= (( incident(b2, a3a1))),
19.06/19.36	    inference('demod', [status(thm)], ['221', '222'])).
19.06/19.36	tff('224', plain,
19.06/19.36	    ((sk_C_1(b2, b3) = a3a1 | b2 = p2))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['207', '223'])).
19.06/19.36	tff('225', plain,
19.06/19.36	    (p2 = b3) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['137', '138'])).
19.06/19.36	tff('226', plain,
19.06/19.36	    ((sk_C_1(b2, b3) = a3a1 | b2 = b3))
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['224', '225'])).
19.06/19.36	tff('227', plain, b3 != b2,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['94', '96'])).
19.06/19.36	tff('228', plain,
19.06/19.36	    (sk_C_1(b2, b3) = a3a1)
19.06/19.36	      <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['226', '227'])).
19.06/19.36	tff('229', plain,  incident(a3, a3a1),
19.06/19.36	    inference('cnf', [status(esa)], [ia3a1])).
19.06/19.36	tff('230', plain,
19.06/19.36	    (a3 = b3) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['188', '205', '206', '228', '229'])).
19.06/19.36	tff('231', plain,  incident(b3, b3b1),
19.06/19.36	    inference('cnf', [status(esa)], [ib3b1])).
19.06/19.36	tff('232', plain,
19.06/19.36	    ( incident(a3, b3b1)) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup+', [status(thm)], ['230', '231'])).
19.06/19.36	tff('233', plain,  incident(a3, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ia3a2])).
19.06/19.36	tff('234', plain,  incident(b1, b3b1),
19.06/19.36	    inference('cnf', [status(esa)], [ib1b3])).
19.06/19.36	tff(gap2, axiom, (incident(b1,a2a3) | incident(a2,b3b1))).
19.06/19.36	tff('235', plain, ( incident(b1, a2a3) |  incident(a2, b3b1)),
19.06/19.36	    inference('cnf', [status(esa)], [gap2])).
19.06/19.36	tff('236', plain, ( incident(b1, a2a3)) <= (( incident(b1, a2a3))),
19.06/19.36	    inference('split', [status(esa)], ['235'])).
19.06/19.36	tff('237', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('238', plain,
19.06/19.36	    (![X0, X1]:
19.06/19.36	       (a2a3 = X0
19.06/19.36	        | ~ incident(b1, X0)
19.06/19.36	        | ~ incident(X1, X0)
19.06/19.36	        | ~ incident(X1, a2a3)
19.06/19.36	        | b1 = X1))
19.06/19.36	      <= (( incident(b1, a2a3))),
19.06/19.36	    inference('sup-', [status(thm)], ['236', '237'])).
19.06/19.36	tff('239', plain,
19.06/19.36	    (![X0]:
19.06/19.36	       (b1 = X0 | ~ incident(X0, a2a3) | ~ incident(X0, b3b1) | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3))),
19.06/19.36	    inference('sup-', [status(thm)], ['234', '238'])).
19.06/19.36	tff('240', plain,
19.06/19.36	    ((a2a3 = b3b1 | ~ incident(a3, b3b1) | b1 = a3))
19.06/19.36	      <= (( incident(b1, a2a3))),
19.06/19.36	    inference('sup-', [status(thm)], ['233', '239'])).
19.06/19.36	tff('241', plain,
19.06/19.36	    ((b1 = a3 | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & 
19.06/19.36	          ( incident(b2, a3a1)) & 
19.06/19.36	          ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['232', '240'])).
19.06/19.36	tff('242', plain,
19.06/19.36	    (a3 = b3) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('demod', [status(thm)], ['188', '205', '206', '228', '229'])).
19.06/19.36	tff('243', plain, b1 != b3, inference('clc', [status(thm)], ['141', '142'])).
19.06/19.36	tff('244', plain,
19.06/19.36	    (b1 != a3) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['242', '243'])).
19.06/19.36	tff('245', plain,
19.06/19.36	    (a2a3 = b3b1)
19.06/19.36	      <= (( incident(b1, a2a3)) & 
19.06/19.36	          ( incident(b2, a3a1)) & 
19.06/19.36	          ( incident(a1, b2b3))),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['241', '244'])).
19.06/19.36	tff('246', plain, (~ incident(a2, b3b1)) <= (~ ( incident(a2, b3b1))),
19.06/19.36	    inference('split', [status(esa)], ['0'])).
19.06/19.36	tff('247', plain,
19.06/19.36	    (~ incident(a2, a2a3))
19.06/19.36	      <= (~ ( incident(a2, b3b1)) & 
19.06/19.36	          ( incident(b1, a2a3)) & 
19.06/19.36	          ( incident(b2, a3a1)) & 
19.06/19.36	          ( incident(a1, b2b3))),
19.06/19.36	    inference('sup-', [status(thm)], ['245', '246'])).
19.06/19.36	tff(ia2a3, axiom, (incident(a2,a2a3))).
19.06/19.36	tff('248', plain,  incident(a2, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ia2a3])).
19.06/19.36	tff('249', plain,
19.06/19.36	    ~ ( incident(b2, a3a1)) | ~ ( incident(a1, b2b3)) | 
19.06/19.36	    ~ ( incident(b1, a2a3)) | ( incident(a2, b3b1)),
19.06/19.36	    inference('demod', [status(thm)], ['247', '248'])).
19.06/19.36	tff(t_b_in_a, axiom,
19.06/19.36	  ((incident(b1,a2a3) & incident(b2,a3a1) & incident(b3,a1a2)) => goal)).
19.06/19.36	tff('250', plain,
19.06/19.36	    ( goal
19.06/19.36	     | ~ incident(b3, a1a2)
19.06/19.36	     | ~ incident(b2, a3a1)
19.06/19.36	     | ~ incident(b1, a2a3)),
19.06/19.36	    inference('cnf', [status(esa)], [t_b_in_a])).
19.06/19.36	tff('251', plain,
19.06/19.36	    ~ ( incident(b3, a1a2)) | ~ ( incident(b2, a3a1)) | ( goal) | 
19.06/19.36	    ~ ( incident(b1, a2a3)), inference('split', [status(esa)], ['250'])).
19.06/19.36	tff('252', plain,
19.06/19.36	    ![X16, X17]:
19.06/19.36	      (~ point(X16) | ~ point(X17) |  incident(X16, sk_C_1(X17, X16))),
19.06/19.36	    inference('cnf', [status(esa)], [join])).
19.06/19.36	tff('253', plain, ( incident(a2, b3b1)) <= (( incident(a2, b3b1))),
19.06/19.36	    inference('split', [status(esa)], ['235'])).
19.06/19.36	tff('254', plain,  incident(a2, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ia2a3])).
19.06/19.36	tff('255', plain,
19.06/19.36	    (![X0]:
19.06/19.36	       (b1 = X0 | ~ incident(X0, a2a3) | ~ incident(X0, b3b1) | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3))),
19.06/19.36	    inference('sup-', [status(thm)], ['234', '238'])).
19.06/19.36	tff('256', plain,
19.06/19.36	    ((a2a3 = b3b1 | ~ incident(a2, b3b1) | b1 = a2))
19.06/19.36	      <= (( incident(b1, a2a3))),
19.06/19.36	    inference('sup-', [status(thm)], ['254', '255'])).
19.06/19.36	tff('257', plain,
19.06/19.36	    ((b1 = a2 | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['253', '256'])).
19.06/19.36	tff('258', plain, (a1a2 = s1 | ~ incident(a2, s1)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['52', '57'])).
19.06/19.36	tff('259', plain,
19.06/19.36	    ((~ incident(b1, s1) | a2a3 = b3b1 | a1a2 = s1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['257', '258'])).
19.06/19.36	tff('260', plain,  incident(b1, s1), inference('cnf', [status(esa)], [ib1s1])).
19.06/19.36	tff('261', plain,
19.06/19.36	    ((a2a3 = b3b1 | a1a2 = s1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('demod', [status(thm)], ['259', '260'])).
19.06/19.36	tff('262', plain,
19.06/19.36	    ((b1 = a2 | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['253', '256'])).
19.06/19.36	tff('263', plain,  incident(a2, s2), inference('cnf', [status(esa)], [ia2s2])).
19.06/19.36	tff('264', plain,
19.06/19.36	    (( incident(b1, s2) | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup+', [status(thm)], ['262', '263'])).
19.06/19.36	tff('265', plain,  incident(b2, b1b2),
19.06/19.36	    inference('cnf', [status(esa)], [ib2b1])).
19.06/19.36	tff('266', plain,  incident(b2, s2), inference('cnf', [status(esa)], [ib2s2])).
19.06/19.36	tff('267', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('268', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (s2 = X0
19.06/19.36	       | ~ incident(b2, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, s2)
19.06/19.36	       | b2 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['266', '267'])).
19.06/19.36	tff('269', plain,
19.06/19.36	    ![X0]: (b2 = X0 | ~ incident(X0, s2) | ~ incident(X0, b1b2) | s2 = b1b2),
19.06/19.36	    inference('sup-', [status(thm)], ['265', '268'])).
19.06/19.36	tff('270', plain,
19.06/19.36	    ((a2a3 = b3b1 | s2 = b1b2 | ~ incident(b1, b1b2) | b2 = b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['264', '269'])).
19.06/19.36	tff('271', plain,  incident(b1, b1b2),
19.06/19.36	    inference('cnf', [status(esa)], [ib1b2])).
19.06/19.36	tff('272', plain,
19.06/19.36	    ((a2a3 = b3b1 | s2 = b1b2 | b2 = b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('demod', [status(thm)], ['270', '271'])).
19.06/19.36	tff('273', plain, b1 != b2,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['25', '31'])).
19.06/19.36	tff('274', plain,
19.06/19.36	    ((a2a3 = b3b1 | s2 = b1b2))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['272', '273'])).
19.06/19.36	tff('275', plain,  incident(s, s2), inference('cnf', [status(esa)], [iss2])).
19.06/19.36	tff('276', plain,
19.06/19.36	    (( incident(s, b1b2) | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup+', [status(thm)], ['274', '275'])).
19.06/19.36	tff('277', plain,  incident(s, s1), inference('cnf', [status(esa)], [iss1])).
19.06/19.36	tff('278', plain,
19.06/19.36	    ![X0]: (b1 = X0 | ~ incident(X0, s1) | ~ incident(X0, b1b2) | s1 = b1b2),
19.06/19.36	    inference('sup-', [status(thm)], ['16', '19'])).
19.06/19.36	tff('279', plain, (s1 = b1b2 | ~ incident(s, b1b2) | b1 = s),
19.06/19.36	    inference('sup-', [status(thm)], ['277', '278'])).
19.06/19.36	tff('280', plain,
19.06/19.36	    ((a2a3 = b3b1 | b1 = s | s1 = b1b2))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['276', '279'])).
19.06/19.36	tff('281', plain,
19.06/19.36	    ((a1a2 = b1b2 | a2a3 = b3b1 | b1 = s | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup+', [status(thm)], ['261', '280'])).
19.06/19.36	tff('282', plain,
19.06/19.36	    ((b1 = s | a2a3 = b3b1 | a1a2 = b1b2))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('simplify', [status(thm)], ['281'])).
19.06/19.36	tff('283', plain, a1a2 != b1b2,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['65', '67'])).
19.06/19.36	tff('284', plain,
19.06/19.36	    ((b1 = s | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['282', '283'])).
19.06/19.36	tff('285', plain,  incident(s, s3), inference('cnf', [status(esa)], [iss3])).
19.06/19.36	tff('286', plain,
19.06/19.36	    (( incident(b1, s3) | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup+', [status(thm)], ['284', '285'])).
19.06/19.36	tff('287', plain,  incident(b3, b3b1),
19.06/19.36	    inference('cnf', [status(esa)], [ib3b1])).
19.06/19.36	tff('288', plain,  incident(b3, s3), inference('cnf', [status(esa)], [ib3s3])).
19.06/19.36	tff('289', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('290', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (s3 = X0
19.06/19.36	       | ~ incident(b3, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, s3)
19.06/19.36	       | b3 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['288', '289'])).
19.06/19.36	tff('291', plain,
19.06/19.36	    ![X0]: (b3 = X0 | ~ incident(X0, s3) | ~ incident(X0, b3b1) | s3 = b3b1),
19.06/19.36	    inference('sup-', [status(thm)], ['287', '290'])).
19.06/19.36	tff('292', plain,
19.06/19.36	    ((a2a3 = b3b1 | s3 = b3b1 | ~ incident(b1, b3b1) | b3 = b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['286', '291'])).
19.06/19.36	tff('293', plain,  incident(b1, b3b1),
19.06/19.36	    inference('cnf', [status(esa)], [ib1b3])).
19.06/19.36	tff('294', plain,
19.06/19.36	    ((a2a3 = b3b1 | s3 = b3b1 | b3 = b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('demod', [status(thm)], ['292', '293'])).
19.06/19.36	tff('295', plain, b1 != b3, inference('clc', [status(thm)], ['141', '142'])).
19.06/19.36	tff('296', plain,
19.06/19.36	    ((a2a3 = b3b1 | s3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['294', '295'])).
19.06/19.36	tff('297', plain,  incident(a3, s3), inference('cnf', [status(esa)], [ia3s3])).
19.06/19.36	tff('298', plain,
19.06/19.36	    (( incident(a3, b3b1) | a2a3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup+', [status(thm)], ['296', '297'])).
19.06/19.36	tff('299', plain,  incident(a3, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ia3a2])).
19.06/19.36	tff('300', plain, ( incident(a2, b3b1)) <= (( incident(a2, b3b1))),
19.06/19.36	    inference('split', [status(esa)], ['235'])).
19.06/19.36	tff('301', plain,  incident(a2, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ia2a3])).
19.06/19.36	tff('302', plain,
19.06/19.36	    ![X18, X19, X20, X21]:
19.06/19.36	      (X19 = X18
19.06/19.36	       | ~ incident(X19, X20)
19.06/19.36	       | ~ incident(X18, X20)
19.06/19.36	       | ~ incident(X18, X21)
19.06/19.36	       | ~ incident(X19, X21)
19.06/19.36	       | X20 = X21),
19.06/19.36	    inference('cnf', [status(esa)], [unique])).
19.06/19.36	tff('303', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (a2a3 = X0
19.06/19.36	       | ~ incident(a2, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, a2a3)
19.06/19.36	       | a2 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['301', '302'])).
19.06/19.36	tff('304', plain,
19.06/19.36	    (![X0]:
19.06/19.36	       (a2 = X0 | ~ incident(X0, a2a3) | ~ incident(X0, b3b1) | a2a3 = b3b1))
19.06/19.36	      <= (( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['300', '303'])).
19.06/19.36	tff('305', plain,
19.06/19.36	    ((a2a3 = b3b1 | ~ incident(a3, b3b1) | a2 = a3))
19.06/19.36	      <= (( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['299', '304'])).
19.06/19.36	tff(diff_a2_a3, axiom, ((a3 = a2) => goal)).
19.06/19.36	tff('306', plain, ( goal | a3 != a2),
19.06/19.36	    inference('cnf', [status(esa)], [diff_a2_a3])).
19.06/19.36	tff('307', plain, ~ goal, inference('cnf', [status(esa)], [zf_stmt_0])).
19.06/19.36	tff('308', plain, a3 != a2, inference('clc', [status(thm)], ['306', '307'])).
19.06/19.36	tff('309', plain,
19.06/19.36	    ((a2a3 = b3b1 | ~ incident(a3, b3b1))) <= (( incident(a2, b3b1))),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['305', '308'])).
19.06/19.36	tff('310', plain,
19.06/19.36	    (a2a3 = b3b1) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('clc', [status(thm)], ['298', '309'])).
19.06/19.36	tff('311', plain,  incident(p1, b2b3),
19.06/19.36	    inference('cnf', [status(esa)], [ip1b])).
19.06/19.36	tff('312', plain,  incident(b3, b3b1),
19.06/19.36	    inference('cnf', [status(esa)], [ib3b1])).
19.06/19.36	tff('313', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (b2b3 = X0
19.06/19.36	       | ~ incident(b3, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, b2b3)
19.06/19.36	       | b3 = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['88', '89'])).
19.06/19.36	tff('314', plain,
19.06/19.36	    ![X0]:
19.06/19.36	      (b3 = X0 | ~ incident(X0, b2b3) | ~ incident(X0, b3b1) | b2b3 = b3b1),
19.06/19.36	    inference('sup-', [status(thm)], ['312', '313'])).
19.06/19.36	tff('315', plain, (b2b3 = b3b1 | ~ incident(p1, b3b1) | b3 = p1),
19.06/19.36	    inference('sup-', [status(thm)], ['311', '314'])).
19.06/19.36	tff('316', plain,
19.06/19.36	    ((~ incident(p1, a2a3) | b3 = p1 | b2b3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['310', '315'])).
19.06/19.36	tff('317', plain,  incident(p1, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ip1a])).
19.06/19.36	tff('318', plain,
19.06/19.36	    (a2a3 = b3b1) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('clc', [status(thm)], ['298', '309'])).
19.06/19.36	tff('319', plain,
19.06/19.36	    ((b3 = p1 | b2b3 = a2a3))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('demod', [status(thm)], ['316', '317', '318'])).
19.06/19.36	tff('320', plain, a2a3 != b2b3,
19.06/19.36	    inference('simpl_trail', [status(thm)], ['197', '199'])).
19.06/19.36	tff('321', plain,
19.06/19.36	    (b3 = p1) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['319', '320'])).
19.06/19.36	tff('322', plain, ~ incident(p1, sk_C_1(p3, p2)),
19.06/19.36	    inference('demod', [status(thm)], ['181', '182', '185', '186'])).
19.06/19.36	tff('323', plain,
19.06/19.36	    (~ incident(b3, sk_C_1(p3, p2)))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['321', '322'])).
19.06/19.36	tff('324', plain,
19.06/19.36	    (a2a3 = b3b1) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('clc', [status(thm)], ['298', '309'])).
19.06/19.36	tff('325', plain,  incident(a3, a3a1),
19.06/19.36	    inference('cnf', [status(esa)], [ia3a1])).
19.06/19.36	tff('326', plain,
19.06/19.36	    ![X0]: (p2 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, b3b1)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['126', '131'])).
19.06/19.36	tff('327', plain, (~ incident(a3, b3b1) | p2 = a3),
19.06/19.36	    inference('sup-', [status(thm)], ['325', '326'])).
19.06/19.36	tff('328', plain,
19.06/19.36	    ((~ incident(a3, a2a3) | p2 = a3))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['324', '327'])).
19.06/19.36	tff('329', plain,  incident(a3, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ia3a2])).
19.06/19.36	tff('330', plain,
19.06/19.36	    (p2 = a3) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('demod', [status(thm)], ['328', '329'])).
19.06/19.36	tff('331', plain,
19.06/19.36	    (~ incident(b3, sk_C_1(p3, a3)))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('demod', [status(thm)], ['323', '330'])).
19.06/19.36	tff('332', plain,
19.06/19.36	    (a2a3 = b3b1) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('clc', [status(thm)], ['298', '309'])).
19.06/19.36	tff('333', plain,  incident(a3, s3), inference('cnf', [status(esa)], [ia3s3])).
19.06/19.36	tff('334', plain,
19.06/19.36	    ![X0]: (b3 = X0 | ~ incident(X0, s3) | ~ incident(X0, b3b1) | s3 = b3b1),
19.06/19.36	    inference('sup-', [status(thm)], ['287', '290'])).
19.06/19.36	tff('335', plain, (s3 = b3b1 | ~ incident(a3, b3b1) | b3 = a3),
19.06/19.36	    inference('sup-', [status(thm)], ['333', '334'])).
19.06/19.36	tff('336', plain,
19.06/19.36	    ((~ incident(a3, a2a3) | b3 = a3 | s3 = b3b1))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['332', '335'])).
19.06/19.36	tff('337', plain,  incident(a3, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ia3a2])).
19.06/19.36	tff('338', plain,
19.06/19.36	    (a2a3 = b3b1) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('clc', [status(thm)], ['298', '309'])).
19.06/19.36	tff('339', plain,
19.06/19.36	    ((b3 = a3 | s3 = a2a3))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('demod', [status(thm)], ['336', '337', '338'])).
19.06/19.36	tff('340', plain,
19.06/19.36	    ((b3 = a3 | s3 = a2a3))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('demod', [status(thm)], ['336', '337', '338'])).
19.06/19.36	tff('341', plain,  incident(a2, s2), inference('cnf', [status(esa)], [ia2s2])).
19.06/19.36	tff('342', plain,  incident(s, s3), inference('cnf', [status(esa)], [iss3])).
19.06/19.36	tff('343', plain,
19.06/19.36	    ![X0, X1]:
19.06/19.36	      (s2 = X0
19.06/19.36	       | ~ incident(s, X0)
19.06/19.36	       | ~ incident(X1, X0)
19.06/19.36	       | ~ incident(X1, s2)
19.06/19.36	       | s = X1),
19.06/19.36	    inference('sup-', [status(thm)], ['39', '40'])).
19.06/19.36	tff('344', plain,
19.06/19.36	    ![X0]: (s = X0 | ~ incident(X0, s2) | ~ incident(X0, s3) | s2 = s3),
19.06/19.36	    inference('sup-', [status(thm)], ['342', '343'])).
19.06/19.36	tff('345', plain, (s2 = s3 | ~ incident(a2, s3) | s = a2),
19.06/19.36	    inference('sup-', [status(thm)], ['341', '344'])).
19.06/19.36	tff('346', plain,
19.06/19.36	    ((~ incident(a2, a2a3) | b3 = a3 | s = a2 | s2 = s3))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['340', '345'])).
19.06/19.36	tff('347', plain,  incident(a2, a2a3),
19.06/19.36	    inference('cnf', [status(esa)], [ia2a3])).
19.06/19.36	tff('348', plain,
19.06/19.36	    ((b3 = a3 | s = a2 | s2 = s3))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('demod', [status(thm)], ['346', '347'])).
19.06/19.36	tff('349', plain, (b2b3 = s3 | ~ incident(b2, s3)),
19.06/19.36	    inference('simplify_reflect-', [status(thm)], ['92', '97'])).
19.06/19.36	tff('350', plain,
19.06/19.36	    ((~ incident(b2, s2) | s = a2 | b3 = a3 | b2b3 = s3))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('sup-', [status(thm)], ['348', '349'])).
19.06/19.36	tff('351', plain,  incident(b2, s2), inference('cnf', [status(esa)], [ib2s2])).
19.06/19.36	tff('352', plain,
19.06/19.36	    ((s = a2 | b3 = a3 | b2b3 = s3))
19.06/19.36	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.36	    inference('demod', [status(thm)], ['350', '351'])).
19.06/19.36	tff('353', plain,
19.06/19.37	    ((b2b3 = a2a3 | b3 = a3 | b3 = a3 | s = a2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['339', '352'])).
19.06/19.37	tff('354', plain,
19.06/19.37	    ((s = a2 | b3 = a3 | b2b3 = a2a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['353'])).
19.06/19.37	tff('355', plain, a2a3 != b2b3,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['197', '199'])).
19.06/19.37	tff('356', plain,
19.06/19.37	    ((s = a2 | b3 = a3)) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['354', '355'])).
19.06/19.37	tff('357', plain,
19.06/19.37	    ((b3 = a3 | s3 = a2a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['336', '337', '338'])).
19.06/19.37	tff('358', plain,  incident(s, s3), inference('cnf', [status(esa)], [iss3])).
19.06/19.37	tff('359', plain,
19.06/19.37	    (( incident(s, a2a3) | b3 = a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['357', '358'])).
19.06/19.37	tff('360', plain,  incident(b1, s1), inference('cnf', [status(esa)], [ib1s1])).
19.06/19.37	tff('361', plain,
19.06/19.37	    (![X0, X1]:
19.06/19.37	       (a2a3 = X0
19.06/19.37	        | ~ incident(b1, X0)
19.06/19.37	        | ~ incident(X1, X0)
19.06/19.37	        | ~ incident(X1, a2a3)
19.06/19.37	        | b1 = X1))
19.06/19.37	      <= (( incident(b1, a2a3))),
19.06/19.37	    inference('sup-', [status(thm)], ['236', '237'])).
19.06/19.37	tff('362', plain,
19.06/19.37	    (![X0]: (b1 = X0 | ~ incident(X0, a2a3) | ~ incident(X0, s1) | a2a3 = s1))
19.06/19.37	      <= (( incident(b1, a2a3))),
19.06/19.37	    inference('sup-', [status(thm)], ['360', '361'])).
19.06/19.37	tff('363', plain,
19.06/19.37	    ((b3 = a3 | a2a3 = s1 | ~ incident(s, s1) | b1 = s))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['359', '362'])).
19.06/19.37	tff('364', plain,  incident(s, s1), inference('cnf', [status(esa)], [iss1])).
19.06/19.37	tff('365', plain,
19.06/19.37	    ((b3 = a3 | a2a3 = s1 | b1 = s))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['363', '364'])).
19.06/19.37	tff('366', plain,
19.06/19.37	    ((b3 = a3 | a2a3 = s1 | b1 = s))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['363', '364'])).
19.06/19.37	tff('367', plain,  incident(p2, a3a1),
19.06/19.37	    inference('cnf', [status(esa)], [ip2a])).
19.06/19.37	tff('368', plain,
19.06/19.37	    ![X0]: (a1 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, s1) | a3a1 = s1),
19.06/19.37	    inference('sup-', [status(thm)], ['112', '115'])).
19.06/19.37	tff('369', plain, (a3a1 = s1 | ~ incident(p2, s1) | a1 = p2),
19.06/19.37	    inference('sup-', [status(thm)], ['367', '368'])).
19.06/19.37	tff('370', plain,
19.06/19.37	    ((~ incident(p2, a2a3) | b1 = s | b3 = a3 | a1 = p2 | a3a1 = s1))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['366', '369'])).
19.06/19.37	tff('371', plain,
19.06/19.37	    (p2 = a3) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['328', '329'])).
19.06/19.37	tff('372', plain,  incident(a3, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia3a2])).
19.06/19.37	tff('373', plain,
19.06/19.37	    (p2 = a3) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['328', '329'])).
19.06/19.37	tff('374', plain,
19.06/19.37	    ((b1 = s | b3 = a3 | a1 = a3 | a3a1 = s1))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['370', '371', '372', '373'])).
19.06/19.37	tff('375', plain, a1 != a3, inference('clc', [status(thm)], ['79', '80'])).
19.06/19.37	tff('376', plain,
19.06/19.37	    ((b1 = s | b3 = a3 | a3a1 = s1))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['374', '375'])).
19.06/19.37	tff('377', plain,
19.06/19.37	    ((a3a1 = a2a3 | b1 = s | b3 = a3 | b3 = a3 | b1 = s))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['365', '376'])).
19.06/19.37	tff('378', plain,
19.06/19.37	    ((b3 = a3 | b1 = s | a3a1 = a2a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['377'])).
19.06/19.37	tff('379', plain,
19.06/19.37	    (a2a3 = b3b1) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('clc', [status(thm)], ['298', '309'])).
19.06/19.37	tff('380', plain, b3b1 != a3a1,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['128', '130'])).
19.06/19.37	tff('381', plain,
19.06/19.37	    (a2a3 != a3a1) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['379', '380'])).
19.06/19.37	tff('382', plain,
19.06/19.37	    ((b3 = a3 | b1 = s)) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['378', '381'])).
19.06/19.37	tff('383', plain,
19.06/19.37	    ((b1 = a2 | b3 = a3 | b3 = a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['356', '382'])).
19.06/19.37	tff('384', plain,
19.06/19.37	    ((b3 = a3 | b1 = a2)) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['383'])).
19.06/19.37	tff('385', plain,  incident(a2, a1a2),
19.06/19.37	    inference('cnf', [status(esa)], [ia2a1])).
19.06/19.37	tff('386', plain,
19.06/19.37	    ![X0]: (p3 = X0 | ~ incident(X0, a1a2) | ~ incident(X0, b1b2)),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['163', '164'])).
19.06/19.37	tff('387', plain, (~ incident(a2, b1b2) | p3 = a2),
19.06/19.37	    inference('sup-', [status(thm)], ['385', '386'])).
19.06/19.37	tff('388', plain,
19.06/19.37	    ((~ incident(b1, b1b2) | b3 = a3 | p3 = a2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['384', '387'])).
19.06/19.37	tff('389', plain,  incident(b1, b1b2),
19.06/19.37	    inference('cnf', [status(esa)], [ib1b2])).
19.06/19.37	tff('390', plain,
19.06/19.37	    ((b3 = a3 | p3 = a2)) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['388', '389'])).
19.06/19.37	tff('391', plain, ~ incident(p1, sk_C_1(p3, p2)),
19.06/19.37	    inference('demod', [status(thm)], ['181', '182', '185', '186'])).
19.06/19.37	tff('392', plain,
19.06/19.37	    ((~ incident(p1, sk_C_1(a2, p2)) | b3 = a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['390', '391'])).
19.06/19.37	tff('393', plain,
19.06/19.37	    (b3 = p1) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['319', '320'])).
19.06/19.37	tff('394', plain,
19.06/19.37	    (p2 = a3) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['328', '329'])).
19.06/19.37	tff('395', plain,  incident(a3, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia3a2])).
19.06/19.37	tff('396', plain,  incident(a2, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia2a3])).
19.06/19.37	tff('397', plain,
19.06/19.37	    ![X0, X1, X2]:
19.06/19.37	      (sk_C_1(X1, X0) = X2
19.06/19.37	       | ~ incident(X1, X2)
19.06/19.37	       | ~ incident(X0, X2)
19.06/19.37	       | X1 = X0
19.06/19.37	       | ~ point(X0)
19.06/19.37	       | ~ point(X1)),
19.06/19.37	    inference('simplify', [status(thm)], ['214'])).
19.06/19.37	tff('398', plain,
19.06/19.37	    ![X0]:
19.06/19.37	      (~ point(a2)
19.06/19.37	       | ~ point(X0)
19.06/19.37	       | a2 = X0
19.06/19.37	       | ~ incident(X0, a2a3)
19.06/19.37	       | sk_C_1(a2, X0) = a2a3),
19.06/19.37	    inference('sup-', [status(thm)], ['396', '397'])).
19.06/19.37	tff('399', plain,  incident(a2, a1a2),
19.06/19.37	    inference('cnf', [status(esa)], [ia2a1])).
19.06/19.37	tff('400', plain, ![X11, X12]: ( point(X11) | ~ incident(X11, X12)),
19.06/19.37	    inference('cnf', [status(esa)], [sort_point])).
19.06/19.37	tff('401', plain,  point(a2),
19.06/19.37	    inference('sup-', [status(thm)], ['399', '400'])).
19.06/19.37	tff('402', plain,
19.06/19.37	    ![X0]:
19.06/19.37	      (~ point(X0) | a2 = X0 | ~ incident(X0, a2a3) | sk_C_1(a2, X0) = a2a3),
19.06/19.37	    inference('demod', [status(thm)], ['398', '401'])).
19.06/19.37	tff('403', plain, (sk_C_1(a2, a3) = a2a3 | a2 = a3 | ~ point(a3)),
19.06/19.37	    inference('sup-', [status(thm)], ['395', '402'])).
19.06/19.37	tff('404', plain,  incident(a3, a3a1),
19.06/19.37	    inference('cnf', [status(esa)], [ia3a1])).
19.06/19.37	tff('405', plain, ![X11, X12]: ( point(X11) | ~ incident(X11, X12)),
19.06/19.37	    inference('cnf', [status(esa)], [sort_point])).
19.06/19.37	tff('406', plain,  point(a3),
19.06/19.37	    inference('sup-', [status(thm)], ['404', '405'])).
19.06/19.37	tff('407', plain, (sk_C_1(a2, a3) = a2a3 | a2 = a3),
19.06/19.37	    inference('demod', [status(thm)], ['403', '406'])).
19.06/19.37	tff('408', plain, a3 != a2, inference('clc', [status(thm)], ['306', '307'])).
19.06/19.37	tff('409', plain, sk_C_1(a2, a3) = a2a3,
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['407', '408'])).
19.06/19.37	tff('410', plain,
19.06/19.37	    (a2a3 = b3b1) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('clc', [status(thm)], ['298', '309'])).
19.06/19.37	tff('411', plain,  incident(b3, b3b1),
19.06/19.37	    inference('cnf', [status(esa)], [ib3b1])).
19.06/19.37	tff('412', plain,
19.06/19.37	    ( incident(b3, a2a3)) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['410', '411'])).
19.06/19.37	tff('413', plain,
19.06/19.37	    (b3 = a3) <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['392', '393', '394', '409', '412'])).
19.06/19.37	tff('414', plain,
19.06/19.37	    (~ incident(a3, sk_C_1(p3, a3)))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['331', '413'])).
19.06/19.37	tff('415', plain,
19.06/19.37	    ((~ point(p3) | ~ point(a3)))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['252', '414'])).
19.06/19.37	tff('416', plain,  point(p3),
19.06/19.37	    inference('sup-', [status(thm)], ['177', '178'])).
19.06/19.37	tff('417', plain,  point(a3),
19.06/19.37	    inference('sup-', [status(thm)], ['404', '405'])).
19.06/19.37	tff('418', plain, ~ ( incident(b1, a2a3)) | ~ ( incident(a2, b3b1)),
19.06/19.37	    inference('demod', [status(thm)], ['415', '416', '417'])).
19.06/19.37	tff('419', plain,
19.06/19.37	    ![X16, X17]:
19.06/19.37	      (~ point(X16) | ~ point(X17) |  incident(X17, sk_C_1(X17, X16))),
19.06/19.37	    inference('cnf', [status(esa)], [join])).
19.06/19.37	tff('420', plain, ( incident(b1, a2a3)) <= (( incident(b1, a2a3))),
19.06/19.37	    inference('split', [status(esa)], ['235'])).
19.06/19.37	tff('421', plain, ( incident(a3, b1b2)) <= (( incident(a3, b1b2))),
19.06/19.37	    inference('split', [status(esa)], ['2'])).
19.06/19.37	tff('422', plain,  incident(a3, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia3a2])).
19.06/19.37	tff('423', plain,
19.06/19.37	    ![X18, X19, X20, X21]:
19.06/19.37	      (X19 = X18
19.06/19.37	       | ~ incident(X19, X20)
19.06/19.37	       | ~ incident(X18, X20)
19.06/19.37	       | ~ incident(X18, X21)
19.06/19.37	       | ~ incident(X19, X21)
19.06/19.37	       | X20 = X21),
19.06/19.37	    inference('cnf', [status(esa)], [unique])).
19.06/19.37	tff('424', plain,
19.06/19.37	    ![X0, X1]:
19.06/19.37	      (a2a3 = X0
19.06/19.37	       | ~ incident(a3, X0)
19.06/19.37	       | ~ incident(X1, X0)
19.06/19.37	       | ~ incident(X1, a2a3)
19.06/19.37	       | a3 = X1),
19.06/19.37	    inference('sup-', [status(thm)], ['422', '423'])).
19.06/19.37	tff('425', plain,
19.06/19.37	    (![X0]:
19.06/19.37	       (a3 = X0 | ~ incident(X0, a2a3) | ~ incident(X0, b1b2) | a2a3 = b1b2))
19.06/19.37	      <= (( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['421', '424'])).
19.06/19.37	tff('426', plain,
19.06/19.37	    ((a2a3 = b1b2 | ~ incident(b1, b1b2) | a3 = b1))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['420', '425'])).
19.06/19.37	tff('427', plain,  incident(b1, b1b2),
19.06/19.37	    inference('cnf', [status(esa)], [ib1b2])).
19.06/19.37	tff('428', plain,
19.06/19.37	    ((a2a3 = b1b2 | a3 = b1))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['426', '427'])).
19.06/19.37	tff('429', plain,  incident(b1, s1), inference('cnf', [status(esa)], [ib1s1])).
19.06/19.37	tff('430', plain,
19.06/19.37	    (( incident(a3, s1) | a2a3 = b1b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['428', '429'])).
19.06/19.37	tff('431', plain,  incident(a3, a3a1),
19.06/19.37	    inference('cnf', [status(esa)], [ia3a1])).
19.06/19.37	tff('432', plain,
19.06/19.37	    ![X0]: (a1 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, s1) | a3a1 = s1),
19.06/19.37	    inference('sup-', [status(thm)], ['112', '115'])).
19.06/19.37	tff('433', plain, (a3a1 = s1 | ~ incident(a3, s1) | a1 = a3),
19.06/19.37	    inference('sup-', [status(thm)], ['431', '432'])).
19.06/19.37	tff('434', plain, a1 != a3, inference('clc', [status(thm)], ['79', '80'])).
19.06/19.37	tff('435', plain, (a3a1 = s1 | ~ incident(a3, s1)),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['433', '434'])).
19.06/19.37	tff('436', plain,
19.06/19.37	    ((a2a3 = b1b2 | a3a1 = s1))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['430', '435'])).
19.06/19.37	tff('437', plain,  incident(s, s1), inference('cnf', [status(esa)], [iss1])).
19.06/19.37	tff('438', plain,
19.06/19.37	    (( incident(s, a3a1) | a2a3 = b1b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['436', '437'])).
19.06/19.37	tff('439', plain,
19.06/19.37	    ![X0]: (a3 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, s3) | a3a1 = s3),
19.06/19.37	    inference('sup-', [status(thm)], ['73', '76'])).
19.06/19.37	tff('440', plain,
19.06/19.37	    ((a2a3 = b1b2 | a3a1 = s3 | ~ incident(s, s3) | a3 = s))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['438', '439'])).
19.06/19.37	tff('441', plain,  incident(s, s3), inference('cnf', [status(esa)], [iss3])).
19.06/19.37	tff('442', plain,
19.06/19.37	    ((a2a3 = b1b2 | a3a1 = s3 | a3 = s))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['440', '441'])).
19.06/19.37	tff('443', plain,  incident(b3, s3), inference('cnf', [status(esa)], [ib3s3])).
19.06/19.37	tff('444', plain,  incident(a3, s3), inference('cnf', [status(esa)], [ia3s3])).
19.06/19.37	tff('445', plain,
19.06/19.37	    ((a2a3 = b1b2 | a3 = b1))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['426', '427'])).
19.06/19.37	tff('446', plain,  incident(b1, b3b1),
19.06/19.37	    inference('cnf', [status(esa)], [ib1b3])).
19.06/19.37	tff('447', plain,
19.06/19.37	    ![X18, X19, X20, X21]:
19.06/19.37	      (X19 = X18
19.06/19.37	       | ~ incident(X19, X20)
19.06/19.37	       | ~ incident(X18, X20)
19.06/19.37	       | ~ incident(X18, X21)
19.06/19.37	       | ~ incident(X19, X21)
19.06/19.37	       | X20 = X21),
19.06/19.37	    inference('cnf', [status(esa)], [unique])).
19.06/19.37	tff('448', plain,
19.06/19.37	    ![X0, X1]:
19.06/19.37	      (b3b1 = X0
19.06/19.37	       | ~ incident(b1, X0)
19.06/19.37	       | ~ incident(X1, X0)
19.06/19.37	       | ~ incident(X1, b3b1)
19.06/19.37	       | b1 = X1),
19.06/19.37	    inference('sup-', [status(thm)], ['446', '447'])).
19.06/19.37	tff('449', plain,
19.06/19.37	    (![X0, X1]:
19.06/19.37	       (~ incident(a3, X0)
19.06/19.37	        | a2a3 = b1b2
19.06/19.37	        | b1 = X1
19.06/19.37	        | ~ incident(X1, b3b1)
19.06/19.37	        | ~ incident(X1, X0)
19.06/19.37	        | b3b1 = X0))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['445', '448'])).
19.06/19.37	tff('450', plain,
19.06/19.37	    (![X0]:
19.06/19.37	       (b3b1 = s3
19.06/19.37	        | ~ incident(X0, s3)
19.06/19.37	        | ~ incident(X0, b3b1)
19.06/19.37	        | b1 = X0
19.06/19.37	        | a2a3 = b1b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['444', '449'])).
19.06/19.37	tff('451', plain,
19.06/19.37	    ((a2a3 = b1b2 | b1 = b3 | ~ incident(b3, b3b1) | b3b1 = s3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['443', '450'])).
19.06/19.37	tff('452', plain,  incident(b3, b3b1),
19.06/19.37	    inference('cnf', [status(esa)], [ib3b1])).
19.06/19.37	tff('453', plain,
19.06/19.37	    ((a2a3 = b1b2 | b1 = b3 | b3b1 = s3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['451', '452'])).
19.06/19.37	tff('454', plain, b1 != b3, inference('clc', [status(thm)], ['141', '142'])).
19.06/19.37	tff('455', plain,
19.06/19.37	    ((a2a3 = b1b2 | b3b1 = s3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['453', '454'])).
19.06/19.37	tff('456', plain,
19.06/19.37	    ((b3b1 = a3a1 | a3 = s | a2a3 = b1b2 | a2a3 = b1b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['442', '455'])).
19.06/19.37	tff('457', plain,
19.06/19.37	    ((a2a3 = b1b2 | a3 = s | b3b1 = a3a1))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify', [status(thm)], ['456'])).
19.06/19.37	tff('458', plain, b3b1 != a3a1,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['128', '130'])).
19.06/19.37	tff('459', plain,
19.06/19.37	    ((a2a3 = b1b2 | a3 = s))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['457', '458'])).
19.06/19.37	tff('460', plain,  incident(s, s2), inference('cnf', [status(esa)], [iss2])).
19.06/19.37	tff('461', plain,
19.06/19.37	    (( incident(a3, s2) | a2a3 = b1b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['459', '460'])).
19.06/19.37	tff('462', plain,  incident(a2, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia2a3])).
19.06/19.37	tff('463', plain,  incident(a2, s2), inference('cnf', [status(esa)], [ia2s2])).
19.06/19.37	tff('464', plain,
19.06/19.37	    ![X18, X19, X20, X21]:
19.06/19.37	      (X19 = X18
19.06/19.37	       | ~ incident(X19, X20)
19.06/19.37	       | ~ incident(X18, X20)
19.06/19.37	       | ~ incident(X18, X21)
19.06/19.37	       | ~ incident(X19, X21)
19.06/19.37	       | X20 = X21),
19.06/19.37	    inference('cnf', [status(esa)], [unique])).
19.06/19.37	tff('465', plain,
19.06/19.37	    ![X0, X1]:
19.06/19.37	      (s2 = X0
19.06/19.37	       | ~ incident(a2, X0)
19.06/19.37	       | ~ incident(X1, X0)
19.06/19.37	       | ~ incident(X1, s2)
19.06/19.37	       | a2 = X1),
19.06/19.37	    inference('sup-', [status(thm)], ['463', '464'])).
19.06/19.37	tff('466', plain,
19.06/19.37	    ![X0]: (a2 = X0 | ~ incident(X0, s2) | ~ incident(X0, a2a3) | s2 = a2a3),
19.06/19.37	    inference('sup-', [status(thm)], ['462', '465'])).
19.06/19.37	tff('467', plain,
19.06/19.37	    ((a2a3 = b1b2 | s2 = a2a3 | ~ incident(a3, a2a3) | a2 = a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['461', '466'])).
19.06/19.37	tff('468', plain,  incident(a3, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia3a2])).
19.06/19.37	tff('469', plain,
19.06/19.37	    ((a2a3 = b1b2 | s2 = a2a3 | a2 = a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['467', '468'])).
19.06/19.37	tff('470', plain, a3 != a2, inference('clc', [status(thm)], ['306', '307'])).
19.06/19.37	tff('471', plain,
19.06/19.37	    ((a2a3 = b1b2 | s2 = a2a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['469', '470'])).
19.06/19.37	tff('472', plain,  incident(b2, s2), inference('cnf', [status(esa)], [ib2s2])).
19.06/19.37	tff('473', plain,
19.06/19.37	    (( incident(b2, a2a3) | a2a3 = b1b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['471', '472'])).
19.06/19.37	tff('474', plain,  incident(b1, b1b2),
19.06/19.37	    inference('cnf', [status(esa)], [ib1b2])).
19.06/19.37	tff('475', plain,
19.06/19.37	    (![X0, X1]:
19.06/19.37	       (a2a3 = X0
19.06/19.37	        | ~ incident(b1, X0)
19.06/19.37	        | ~ incident(X1, X0)
19.06/19.37	        | ~ incident(X1, a2a3)
19.06/19.37	        | b1 = X1))
19.06/19.37	      <= (( incident(b1, a2a3))),
19.06/19.37	    inference('sup-', [status(thm)], ['236', '237'])).
19.06/19.37	tff('476', plain,
19.06/19.37	    (![X0]:
19.06/19.37	       (b1 = X0 | ~ incident(X0, a2a3) | ~ incident(X0, b1b2) | a2a3 = b1b2))
19.06/19.37	      <= (( incident(b1, a2a3))),
19.06/19.37	    inference('sup-', [status(thm)], ['474', '475'])).
19.06/19.37	tff('477', plain,
19.06/19.37	    ((a2a3 = b1b2 | a2a3 = b1b2 | ~ incident(b2, b1b2) | b1 = b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['473', '476'])).
19.06/19.37	tff('478', plain,  incident(b2, b1b2),
19.06/19.37	    inference('cnf', [status(esa)], [ib2b1])).
19.06/19.37	tff('479', plain,
19.06/19.37	    ((a2a3 = b1b2 | a2a3 = b1b2 | b1 = b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['477', '478'])).
19.06/19.37	tff('480', plain,
19.06/19.37	    ((b1 = b2 | a2a3 = b1b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify', [status(thm)], ['479'])).
19.06/19.37	tff('481', plain, b1 != b2,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['25', '31'])).
19.06/19.37	tff('482', plain,
19.06/19.37	    (a2a3 = b1b2) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['480', '481'])).
19.06/19.37	tff('483', plain,  incident(p1, b2b3),
19.06/19.37	    inference('cnf', [status(esa)], [ip1b])).
19.06/19.37	tff('484', plain,  incident(b2, b1b2),
19.06/19.37	    inference('cnf', [status(esa)], [ib2b1])).
19.06/19.37	tff('485', plain,  incident(b2, b2b3),
19.06/19.37	    inference('cnf', [status(esa)], [ib2b3])).
19.06/19.37	tff('486', plain,
19.06/19.37	    ![X18, X19, X20, X21]:
19.06/19.37	      (X19 = X18
19.06/19.37	       | ~ incident(X19, X20)
19.06/19.37	       | ~ incident(X18, X20)
19.06/19.37	       | ~ incident(X18, X21)
19.06/19.37	       | ~ incident(X19, X21)
19.06/19.37	       | X20 = X21),
19.06/19.37	    inference('cnf', [status(esa)], [unique])).
19.06/19.37	tff('487', plain,
19.06/19.37	    ![X0, X1]:
19.06/19.37	      (b2b3 = X0
19.06/19.37	       | ~ incident(b2, X0)
19.06/19.37	       | ~ incident(X1, X0)
19.06/19.37	       | ~ incident(X1, b2b3)
19.06/19.37	       | b2 = X1),
19.06/19.37	    inference('sup-', [status(thm)], ['485', '486'])).
19.06/19.37	tff('488', plain,
19.06/19.37	    ![X0]:
19.06/19.37	      (b2 = X0 | ~ incident(X0, b2b3) | ~ incident(X0, b1b2) | b2b3 = b1b2),
19.06/19.37	    inference('sup-', [status(thm)], ['484', '487'])).
19.06/19.37	tff('489', plain, (b2b3 = b1b2 | ~ incident(p1, b1b2) | b2 = p1),
19.06/19.37	    inference('sup-', [status(thm)], ['483', '488'])).
19.06/19.37	tff('490', plain,
19.06/19.37	    ((~ incident(p1, a2a3) | b2 = p1 | b2b3 = b1b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['482', '489'])).
19.06/19.37	tff('491', plain,  incident(p1, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ip1a])).
19.06/19.37	tff('492', plain,
19.06/19.37	    (a2a3 = b1b2) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['480', '481'])).
19.06/19.37	tff('493', plain,
19.06/19.37	    ((b2 = p1 | b2b3 = a2a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['490', '491', '492'])).
19.06/19.37	tff('494', plain, a2a3 != b2b3,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['197', '199'])).
19.06/19.37	tff('495', plain,
19.06/19.37	    (b2 = p1) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['493', '494'])).
19.06/19.37	tff('496', plain, ~ incident(p1, sk_C_1(p3, p2)),
19.06/19.37	    inference('demod', [status(thm)], ['181', '182', '185', '186'])).
19.06/19.37	tff('497', plain,
19.06/19.37	    (~ incident(b2, sk_C_1(p3, p2)))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['495', '496'])).
19.06/19.37	tff('498', plain,
19.06/19.37	    (a2a3 = b1b2) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['480', '481'])).
19.06/19.37	tff('499', plain, (~ incident(a2, b1b2) | p3 = a2),
19.06/19.37	    inference('sup-', [status(thm)], ['385', '386'])).
19.06/19.37	tff('500', plain,
19.06/19.37	    ((~ incident(a2, a2a3) | p3 = a2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['498', '499'])).
19.06/19.37	tff('501', plain,  incident(a2, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia2a3])).
19.06/19.37	tff('502', plain,
19.06/19.37	    (p3 = a2) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['500', '501'])).
19.06/19.37	tff('503', plain,
19.06/19.37	    (~ incident(b2, sk_C_1(a2, p2)))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['497', '502'])).
19.06/19.37	tff('504', plain,
19.06/19.37	    (a2a3 = b1b2) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['480', '481'])).
19.06/19.37	tff('505', plain,  incident(a2, s2), inference('cnf', [status(esa)], [ia2s2])).
19.06/19.37	tff('506', plain,
19.06/19.37	    ![X0]: (b2 = X0 | ~ incident(X0, s2) | ~ incident(X0, b1b2) | s2 = b1b2),
19.06/19.37	    inference('sup-', [status(thm)], ['265', '268'])).
19.06/19.37	tff('507', plain, (s2 = b1b2 | ~ incident(a2, b1b2) | b2 = a2),
19.06/19.37	    inference('sup-', [status(thm)], ['505', '506'])).
19.06/19.37	tff('508', plain,
19.06/19.37	    ((~ incident(a2, a2a3) | b2 = a2 | s2 = b1b2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['504', '507'])).
19.06/19.37	tff('509', plain,  incident(a2, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia2a3])).
19.06/19.37	tff('510', plain,
19.06/19.37	    (a2a3 = b1b2) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['480', '481'])).
19.06/19.37	tff('511', plain,
19.06/19.37	    ((b2 = a2 | s2 = a2a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['508', '509', '510'])).
19.06/19.37	tff('512', plain,  incident(s, s2), inference('cnf', [status(esa)], [iss2])).
19.06/19.37	tff('513', plain,
19.06/19.37	    (( incident(s, a2a3) | b2 = a2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['511', '512'])).
19.06/19.37	tff('514', plain,  incident(s, s3), inference('cnf', [status(esa)], [iss3])).
19.06/19.37	tff('515', plain,  incident(a3, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia3a2])).
19.06/19.37	tff('516', plain,  incident(a3, s3), inference('cnf', [status(esa)], [ia3s3])).
19.06/19.37	tff('517', plain,
19.06/19.37	    ![X18, X19, X20, X21]:
19.06/19.37	      (X19 = X18
19.06/19.37	       | ~ incident(X19, X20)
19.06/19.37	       | ~ incident(X18, X20)
19.06/19.37	       | ~ incident(X18, X21)
19.06/19.37	       | ~ incident(X19, X21)
19.06/19.37	       | X20 = X21),
19.06/19.37	    inference('cnf', [status(esa)], [unique])).
19.06/19.37	tff('518', plain,
19.06/19.37	    ![X0, X1]:
19.06/19.37	      (s3 = X0
19.06/19.37	       | ~ incident(a3, X0)
19.06/19.37	       | ~ incident(X1, X0)
19.06/19.37	       | ~ incident(X1, s3)
19.06/19.37	       | a3 = X1),
19.06/19.37	    inference('sup-', [status(thm)], ['516', '517'])).
19.06/19.37	tff('519', plain,
19.06/19.37	    ![X0]: (a3 = X0 | ~ incident(X0, s3) | ~ incident(X0, a2a3) | s3 = a2a3),
19.06/19.37	    inference('sup-', [status(thm)], ['515', '518'])).
19.06/19.37	tff('520', plain, (s3 = a2a3 | ~ incident(s, a2a3) | a3 = s),
19.06/19.37	    inference('sup-', [status(thm)], ['514', '519'])).
19.06/19.37	tff('521', plain,
19.06/19.37	    ((b2 = a2 | a3 = s | s3 = a2a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['513', '520'])).
19.06/19.37	tff('522', plain,
19.06/19.37	    ((b2 = a2 | a3 = s | s3 = a2a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['513', '520'])).
19.06/19.37	tff('523', plain,  incident(p1, b2b3),
19.06/19.37	    inference('cnf', [status(esa)], [ip1b])).
19.06/19.37	tff('524', plain,
19.06/19.37	    ![X0]: (b3 = X0 | ~ incident(X0, b2b3) | ~ incident(X0, s3) | b2b3 = s3),
19.06/19.37	    inference('sup-', [status(thm)], ['87', '90'])).
19.06/19.37	tff('525', plain, (b2b3 = s3 | ~ incident(p1, s3) | b3 = p1),
19.06/19.37	    inference('sup-', [status(thm)], ['523', '524'])).
19.06/19.37	tff('526', plain,
19.06/19.37	    ((~ incident(p1, a2a3) | a3 = s | b2 = a2 | b3 = p1 | b2b3 = s3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['522', '525'])).
19.06/19.37	tff('527', plain,
19.06/19.37	    (b2 = p1) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['493', '494'])).
19.06/19.37	tff('528', plain,
19.06/19.37	    (a2a3 = b1b2) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['480', '481'])).
19.06/19.37	tff('529', plain,  incident(b2, b1b2),
19.06/19.37	    inference('cnf', [status(esa)], [ib2b1])).
19.06/19.37	tff('530', plain,
19.06/19.37	    ( incident(b2, a2a3)) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['528', '529'])).
19.06/19.37	tff('531', plain,
19.06/19.37	    (b2 = p1) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['493', '494'])).
19.06/19.37	tff('532', plain,
19.06/19.37	    ((a3 = s | b2 = a2 | b3 = b2 | b2b3 = s3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['526', '527', '530', '531'])).
19.06/19.37	tff('533', plain, b3 != b2,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['94', '96'])).
19.06/19.37	tff('534', plain,
19.06/19.37	    ((a3 = s | b2 = a2 | b2b3 = s3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['532', '533'])).
19.06/19.37	tff('535', plain,
19.06/19.37	    ((b2b3 = a2a3 | a3 = s | b2 = a2 | b2 = a2 | a3 = s))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['521', '534'])).
19.06/19.37	tff('536', plain,
19.06/19.37	    ((b2 = a2 | a3 = s | b2b3 = a2a3))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify', [status(thm)], ['535'])).
19.06/19.37	tff('537', plain, a2a3 != b2b3,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['197', '199'])).
19.06/19.37	tff('538', plain,
19.06/19.37	    ((b2 = a2 | a3 = s)) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['536', '537'])).
19.06/19.37	tff('539', plain,  incident(s, s1), inference('cnf', [status(esa)], [iss1])).
19.06/19.37	tff('540', plain,
19.06/19.37	    (( incident(a3, s1) | b2 = a2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['538', '539'])).
19.06/19.37	tff('541', plain, (a3a1 = s1 | ~ incident(a3, s1)),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['433', '434'])).
19.06/19.37	tff('542', plain,
19.06/19.37	    ((b2 = a2 | a3a1 = s1))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['540', '541'])).
19.06/19.37	tff('543', plain,  incident(b1, s1), inference('cnf', [status(esa)], [ib1s1])).
19.06/19.37	tff('544', plain,
19.06/19.37	    (( incident(b1, a3a1) | b2 = a2))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['542', '543'])).
19.06/19.37	tff('545', plain,
19.06/19.37	    ![X0]: (p2 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, b3b1)),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['126', '131'])).
19.06/19.37	tff('546', plain,
19.06/19.37	    ((b2 = a2 | ~ incident(b1, b3b1) | p2 = b1))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['544', '545'])).
19.06/19.37	tff('547', plain,  incident(b1, b3b1),
19.06/19.37	    inference('cnf', [status(esa)], [ib1b3])).
19.06/19.37	tff('548', plain,
19.06/19.37	    ((b2 = a2 | p2 = b1)) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['546', '547'])).
19.06/19.37	tff('549', plain,  incident(p3, b1b2),
19.06/19.37	    inference('cnf', [status(esa)], [ip3b])).
19.06/19.37	tff('550', plain,
19.06/19.37	    ![X5]: (~ incident(p3, X5) | ~ incident(p1, X5) | ~ incident(p2, X5)),
19.06/19.37	    inference('simpl_trail', [status(thm)], ['172', '174'])).
19.06/19.37	tff('551', plain, (~ incident(p2, b1b2) | ~ incident(p1, b1b2)),
19.06/19.37	    inference('sup-', [status(thm)], ['549', '550'])).
19.06/19.37	tff('552', plain,
19.06/19.37	    ((~ incident(b1, b1b2) | b2 = a2 | ~ incident(p1, b1b2)))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['548', '551'])).
19.06/19.37	tff('553', plain,
19.06/19.37	    (a2a3 = b1b2) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['480', '481'])).
19.06/19.37	tff('554', plain, ( incident(b1, a2a3)) <= (( incident(b1, a2a3))),
19.06/19.37	    inference('split', [status(esa)], ['235'])).
19.06/19.37	tff('555', plain,
19.06/19.37	    (b2 = p1) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['493', '494'])).
19.06/19.37	tff('556', plain,
19.06/19.37	    (a2a3 = b1b2) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['480', '481'])).
19.06/19.37	tff('557', plain,
19.06/19.37	    ( incident(b2, a2a3)) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup+', [status(thm)], ['528', '529'])).
19.06/19.37	tff('558', plain,
19.06/19.37	    (b2 = a2) <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)],
19.06/19.37	              ['552', '553', '554', '555', '556', '557'])).
19.06/19.37	tff('559', plain,
19.06/19.37	    (~ incident(b2, sk_C_1(b2, p2)))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('demod', [status(thm)], ['503', '558'])).
19.06/19.37	tff('560', plain,
19.06/19.37	    ((~ point(b2) | ~ point(p2)))
19.06/19.37	      <= (( incident(b1, a2a3)) & ( incident(a3, b1b2))),
19.06/19.37	    inference('sup-', [status(thm)], ['419', '559'])).
19.06/19.37	tff('561', plain,  point(b2),
19.06/19.37	    inference('sup-', [status(thm)], ['217', '218'])).
19.06/19.37	tff('562', plain,  point(p2),
19.06/19.37	    inference('sup-', [status(thm)], ['183', '184'])).
19.06/19.37	tff('563', plain, ~ ( incident(a3, b1b2)) | ~ ( incident(b1, a2a3)),
19.06/19.37	    inference('demod', [status(thm)], ['560', '561', '562'])).
19.06/19.37	tff('564', plain, ( incident(a2, b3b1)) | ( incident(b1, a2a3)),
19.06/19.37	    inference('split', [status(esa)], ['235'])).
19.06/19.37	tff('565', plain,
19.06/19.37	    ![X16, X17]:
19.06/19.37	      (~ point(X16) | ~ point(X17) |  incident(X16, sk_C_1(X17, X16))),
19.06/19.37	    inference('cnf', [status(esa)], [join])).
19.06/19.37	tff('566', plain,
19.06/19.37	    ![X16, X17]:
19.06/19.37	      (~ point(X16) | ~ point(X17) |  incident(X17, sk_C_1(X17, X16))),
19.06/19.37	    inference('cnf', [status(esa)], [join])).
19.06/19.37	tff('567', plain, ( incident(a2, b3b1)) <= (( incident(a2, b3b1))),
19.06/19.37	    inference('split', [status(esa)], ['235'])).
19.06/19.37	tff('568', plain,  incident(a2, a1a2),
19.06/19.37	    inference('cnf', [status(esa)], [ia2a1])).
19.06/19.37	tff('569', plain,  incident(b3, b3b1),
19.06/19.37	    inference('cnf', [status(esa)], [ib3b1])).
19.06/19.37	tff('570', plain, ( incident(b3, a1a2)) <= (( incident(b3, a1a2))),
19.06/19.37	    inference('split', [status(esa)], ['6'])).
19.06/19.37	tff('571', plain,
19.06/19.37	    ![X18, X19, X20, X21]:
19.06/19.37	      (X19 = X18
19.06/19.37	       | ~ incident(X19, X20)
19.06/19.37	       | ~ incident(X18, X20)
19.06/19.37	       | ~ incident(X18, X21)
19.06/19.37	       | ~ incident(X19, X21)
19.06/19.37	       | X20 = X21),
19.06/19.37	    inference('cnf', [status(esa)], [unique])).
19.06/19.37	tff('572', plain,
19.06/19.37	    (![X0, X1]:
19.06/19.37	       (a1a2 = X0
19.06/19.37	        | ~ incident(b3, X0)
19.06/19.37	        | ~ incident(X1, X0)
19.06/19.37	        | ~ incident(X1, a1a2)
19.06/19.37	        | b3 = X1))
19.06/19.37	      <= (( incident(b3, a1a2))),
19.06/19.37	    inference('sup-', [status(thm)], ['570', '571'])).
19.06/19.37	tff('573', plain,
19.06/19.37	    (![X0]:
19.06/19.37	       (b3 = X0 | ~ incident(X0, a1a2) | ~ incident(X0, b3b1) | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2))),
19.06/19.37	    inference('sup-', [status(thm)], ['569', '572'])).
19.06/19.37	tff('574', plain,
19.06/19.37	    ((a1a2 = b3b1 | ~ incident(a2, b3b1) | b3 = a2))
19.06/19.37	      <= (( incident(b3, a1a2))),
19.06/19.37	    inference('sup-', [status(thm)], ['568', '573'])).
19.06/19.37	tff('575', plain,
19.06/19.37	    ((b3 = a2 | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['567', '574'])).
19.06/19.37	tff('576', plain,  incident(a2, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia2a3])).
19.06/19.37	tff('577', plain,
19.06/19.37	    (( incident(b3, a2a3) | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['575', '576'])).
19.06/19.37	tff('578', plain,  incident(b3, s3), inference('cnf', [status(esa)], [ib3s3])).
19.06/19.37	tff('579', plain,
19.06/19.37	    ![X0]: (a3 = X0 | ~ incident(X0, s3) | ~ incident(X0, a2a3) | s3 = a2a3),
19.06/19.37	    inference('sup-', [status(thm)], ['515', '518'])).
19.06/19.37	tff('580', plain, (s3 = a2a3 | ~ incident(b3, a2a3) | a3 = b3),
19.06/19.37	    inference('sup-', [status(thm)], ['578', '579'])).
19.06/19.37	tff('581', plain,
19.06/19.37	    ((a1a2 = b3b1 | a3 = b3 | s3 = a2a3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['577', '580'])).
19.06/19.37	tff('582', plain,
19.06/19.37	    ((b3 = a2 | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['567', '574'])).
19.06/19.37	tff('583', plain, a3 != a2, inference('clc', [status(thm)], ['306', '307'])).
19.06/19.37	tff('584', plain,
19.06/19.37	    ((a3 != b3 | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['582', '583'])).
19.06/19.37	tff('585', plain,
19.06/19.37	    ((s3 = a2a3 | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('clc', [status(thm)], ['581', '584'])).
19.06/19.37	tff('586', plain,
19.06/19.37	    ((b3 = a2 | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['567', '574'])).
19.06/19.37	tff('587', plain,  incident(a2, s2), inference('cnf', [status(esa)], [ia2s2])).
19.06/19.37	tff('588', plain,
19.06/19.37	    (( incident(b3, s2) | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['586', '587'])).
19.06/19.37	tff('589', plain,
19.06/19.37	    ![X0]: (s = X0 | ~ incident(X0, s2) | ~ incident(X0, s3) | s2 = s3),
19.06/19.37	    inference('sup-', [status(thm)], ['342', '343'])).
19.06/19.37	tff('590', plain,
19.06/19.37	    ((a1a2 = b3b1 | s2 = s3 | ~ incident(b3, s3) | s = b3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['588', '589'])).
19.06/19.37	tff('591', plain,  incident(b3, s3), inference('cnf', [status(esa)], [ib3s3])).
19.06/19.37	tff('592', plain,
19.06/19.37	    ((a1a2 = b3b1 | s2 = s3 | s = b3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['590', '591'])).
19.06/19.37	tff('593', plain, (b2b3 = s3 | ~ incident(b2, s3)),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['92', '97'])).
19.06/19.37	tff('594', plain,
19.06/19.37	    ((~ incident(b2, s2) | s = b3 | a1a2 = b3b1 | b2b3 = s3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['592', '593'])).
19.06/19.37	tff('595', plain,  incident(b2, s2), inference('cnf', [status(esa)], [ib2s2])).
19.06/19.37	tff('596', plain,
19.06/19.37	    ((s = b3 | a1a2 = b3b1 | b2b3 = s3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['594', '595'])).
19.06/19.37	tff('597', plain,
19.06/19.37	    ((b2b3 = a2a3 | a1a2 = b3b1 | a1a2 = b3b1 | s = b3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['585', '596'])).
19.06/19.37	tff('598', plain,
19.06/19.37	    ((s = b3 | a1a2 = b3b1 | b2b3 = a2a3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['597'])).
19.06/19.37	tff('599', plain, a2a3 != b2b3,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['197', '199'])).
19.06/19.37	tff('600', plain,
19.06/19.37	    ((s = b3 | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['598', '599'])).
19.06/19.37	tff('601', plain,  incident(s, s1), inference('cnf', [status(esa)], [iss1])).
19.06/19.37	tff('602', plain,
19.06/19.37	    (( incident(b3, s1) | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['600', '601'])).
19.06/19.37	tff('603', plain,  incident(b1, b3b1),
19.06/19.37	    inference('cnf', [status(esa)], [ib1b3])).
19.06/19.37	tff('604', plain,
19.06/19.37	    ![X0, X1]:
19.06/19.37	      (s1 = X0
19.06/19.37	       | ~ incident(b1, X0)
19.06/19.37	       | ~ incident(X1, X0)
19.06/19.37	       | ~ incident(X1, s1)
19.06/19.37	       | b1 = X1),
19.06/19.37	    inference('sup-', [status(thm)], ['17', '18'])).
19.06/19.37	tff('605', plain,
19.06/19.37	    ![X0]: (b1 = X0 | ~ incident(X0, s1) | ~ incident(X0, b3b1) | s1 = b3b1),
19.06/19.37	    inference('sup-', [status(thm)], ['603', '604'])).
19.06/19.37	tff('606', plain,
19.06/19.37	    ((a1a2 = b3b1 | s1 = b3b1 | ~ incident(b3, b3b1) | b1 = b3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['602', '605'])).
19.06/19.37	tff('607', plain,  incident(b3, b3b1),
19.06/19.37	    inference('cnf', [status(esa)], [ib3b1])).
19.06/19.37	tff('608', plain,
19.06/19.37	    ((a1a2 = b3b1 | s1 = b3b1 | b1 = b3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['606', '607'])).
19.06/19.37	tff('609', plain, b1 != b3, inference('clc', [status(thm)], ['141', '142'])).
19.06/19.37	tff('610', plain,
19.06/19.37	    ((a1a2 = b3b1 | s1 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['608', '609'])).
19.06/19.37	tff('611', plain,
19.06/19.37	    (( incident(b3, s1) | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['600', '601'])).
19.06/19.37	tff('612', plain,
19.06/19.37	    ((b3 = a2 | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['567', '574'])).
19.06/19.37	tff('613', plain, (a1a2 = s1 | ~ incident(a2, s1)),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['52', '57'])).
19.06/19.37	tff('614', plain,
19.06/19.37	    ((~ incident(b3, s1) | a1a2 = b3b1 | a1a2 = s1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['612', '613'])).
19.06/19.37	tff('615', plain,
19.06/19.37	    ((a1a2 = b3b1 | a1a2 = s1 | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['611', '614'])).
19.06/19.37	tff('616', plain,
19.06/19.37	    ((a1a2 = s1 | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['615'])).
19.06/19.37	tff('617', plain,
19.06/19.37	    ((a1a2 = b3b1 | a1a2 = b3b1 | a1a2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['610', '616'])).
19.06/19.37	tff('618', plain,
19.06/19.37	    (a1a2 = b3b1) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['617'])).
19.06/19.37	tff('619', plain,  incident(p3, b1b2),
19.06/19.37	    inference('cnf', [status(esa)], [ip3b])).
19.06/19.37	tff('620', plain,  incident(b1, b3b1),
19.06/19.37	    inference('cnf', [status(esa)], [ib1b3])).
19.06/19.37	tff('621', plain,  incident(b1, b1b2),
19.06/19.37	    inference('cnf', [status(esa)], [ib1b2])).
19.06/19.37	tff('622', plain,
19.06/19.37	    ![X18, X19, X20, X21]:
19.06/19.37	      (X19 = X18
19.06/19.37	       | ~ incident(X19, X20)
19.06/19.37	       | ~ incident(X18, X20)
19.06/19.37	       | ~ incident(X18, X21)
19.06/19.37	       | ~ incident(X19, X21)
19.06/19.37	       | X20 = X21),
19.06/19.37	    inference('cnf', [status(esa)], [unique])).
19.06/19.37	tff('623', plain,
19.06/19.37	    ![X0, X1]:
19.06/19.37	      (b1b2 = X0
19.06/19.37	       | ~ incident(b1, X0)
19.06/19.37	       | ~ incident(X1, X0)
19.06/19.37	       | ~ incident(X1, b1b2)
19.06/19.37	       | b1 = X1),
19.06/19.37	    inference('sup-', [status(thm)], ['621', '622'])).
19.06/19.37	tff('624', plain,
19.06/19.37	    ![X0]:
19.06/19.37	      (b1 = X0 | ~ incident(X0, b1b2) | ~ incident(X0, b3b1) | b1b2 = b3b1),
19.06/19.37	    inference('sup-', [status(thm)], ['620', '623'])).
19.06/19.37	tff('625', plain, (b1b2 = b3b1 | ~ incident(p3, b3b1) | b1 = p3),
19.06/19.37	    inference('sup-', [status(thm)], ['619', '624'])).
19.06/19.37	tff('626', plain,
19.06/19.37	    ((~ incident(p3, a1a2) | b1 = p3 | b1b2 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['618', '625'])).
19.06/19.37	tff('627', plain,  incident(p3, a1a2),
19.06/19.37	    inference('cnf', [status(esa)], [ip3a])).
19.06/19.37	tff('628', plain,
19.06/19.37	    (a1a2 = b3b1) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['617'])).
19.06/19.37	tff('629', plain,
19.06/19.37	    ((b1 = p3 | b1b2 = a1a2))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['626', '627', '628'])).
19.06/19.37	tff('630', plain, a1a2 != b1b2,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['65', '67'])).
19.06/19.37	tff('631', plain,
19.06/19.37	    (b1 = p3) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['629', '630'])).
19.06/19.37	tff('632', plain,
19.06/19.37	    (a1a2 = b3b1) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['617'])).
19.06/19.37	tff('633', plain,  incident(a1, s1), inference('cnf', [status(esa)], [ia1s1])).
19.06/19.37	tff('634', plain,
19.06/19.37	    ![X0]: (b1 = X0 | ~ incident(X0, s1) | ~ incident(X0, b3b1) | s1 = b3b1),
19.06/19.37	    inference('sup-', [status(thm)], ['603', '604'])).
19.06/19.37	tff('635', plain, (s1 = b3b1 | ~ incident(a1, b3b1) | b1 = a1),
19.06/19.37	    inference('sup-', [status(thm)], ['633', '634'])).
19.06/19.37	tff('636', plain,
19.06/19.37	    ((~ incident(a1, a1a2) | b1 = a1 | s1 = b3b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['632', '635'])).
19.06/19.37	tff('637', plain,  incident(a1, a1a2),
19.06/19.37	    inference('cnf', [status(esa)], [ia1a2])).
19.06/19.37	tff('638', plain,
19.06/19.37	    (a1a2 = b3b1) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['617'])).
19.06/19.37	tff('639', plain,
19.06/19.37	    ((b1 = a1 | s1 = a1a2))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['636', '637', '638'])).
19.06/19.37	tff('640', plain,
19.06/19.37	    ((b1 = a1 | s1 = a1a2))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['636', '637', '638'])).
19.06/19.37	tff('641', plain,  incident(b3, s3), inference('cnf', [status(esa)], [ib3s3])).
19.06/19.37	tff('642', plain,  incident(s, s1), inference('cnf', [status(esa)], [iss1])).
19.06/19.37	tff('643', plain,  incident(s, s3), inference('cnf', [status(esa)], [iss3])).
19.06/19.37	tff('644', plain,
19.06/19.37	    ![X18, X19, X20, X21]:
19.06/19.37	      (X19 = X18
19.06/19.37	       | ~ incident(X19, X20)
19.06/19.37	       | ~ incident(X18, X20)
19.06/19.37	       | ~ incident(X18, X21)
19.06/19.37	       | ~ incident(X19, X21)
19.06/19.37	       | X20 = X21),
19.06/19.37	    inference('cnf', [status(esa)], [unique])).
19.06/19.37	tff('645', plain,
19.06/19.37	    ![X0, X1]:
19.06/19.37	      (s3 = X0
19.06/19.37	       | ~ incident(s, X0)
19.06/19.37	       | ~ incident(X1, X0)
19.06/19.37	       | ~ incident(X1, s3)
19.06/19.37	       | s = X1),
19.06/19.37	    inference('sup-', [status(thm)], ['643', '644'])).
19.06/19.37	tff('646', plain,
19.06/19.37	    ![X0]: (s = X0 | ~ incident(X0, s3) | ~ incident(X0, s1) | s3 = s1),
19.06/19.37	    inference('sup-', [status(thm)], ['642', '645'])).
19.06/19.37	tff('647', plain, (s3 = s1 | ~ incident(b3, s1) | s = b3),
19.06/19.37	    inference('sup-', [status(thm)], ['641', '646'])).
19.06/19.37	tff('648', plain,
19.06/19.37	    ((~ incident(b3, a1a2) | b1 = a1 | s = b3 | s3 = s1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['640', '647'])).
19.06/19.37	tff('649', plain, ( incident(b3, a1a2)) <= (( incident(b3, a1a2))),
19.06/19.37	    inference('split', [status(esa)], ['6'])).
19.06/19.37	tff('650', plain,
19.06/19.37	    ((b1 = a1 | s = b3 | s3 = s1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['648', '649'])).
19.06/19.37	tff('651', plain, (a3a1 = s1 | ~ incident(a3, s1)),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['433', '434'])).
19.06/19.37	tff('652', plain,
19.06/19.37	    ((~ incident(a3, s3) | s = b3 | b1 = a1 | a3a1 = s1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['650', '651'])).
19.06/19.37	tff('653', plain,  incident(a3, s3), inference('cnf', [status(esa)], [ia3s3])).
19.06/19.37	tff('654', plain,
19.06/19.37	    ((s = b3 | b1 = a1 | a3a1 = s1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['652', '653'])).
19.06/19.37	tff('655', plain,
19.06/19.37	    ((a3a1 = a1a2 | b1 = a1 | b1 = a1 | s = b3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['639', '654'])).
19.06/19.37	tff('656', plain,
19.06/19.37	    ((s = b3 | b1 = a1 | a3a1 = a1a2))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['655'])).
19.06/19.37	tff('657', plain,
19.06/19.37	    (a1a2 = b3b1) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['617'])).
19.06/19.37	tff('658', plain, b3b1 != a3a1,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['128', '130'])).
19.06/19.37	tff('659', plain,
19.06/19.37	    (a1a2 != a3a1) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['657', '658'])).
19.06/19.37	tff('660', plain,
19.06/19.37	    ((s = b3 | b1 = a1)) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['656', '659'])).
19.06/19.37	tff('661', plain,  incident(s, s2), inference('cnf', [status(esa)], [iss2])).
19.06/19.37	tff('662', plain,
19.06/19.37	    (( incident(b3, s2) | b1 = a1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['660', '661'])).
19.06/19.37	tff('663', plain,  incident(b2, b2b3),
19.06/19.37	    inference('cnf', [status(esa)], [ib2b3])).
19.06/19.37	tff('664', plain,
19.06/19.37	    ![X0, X1]:
19.06/19.37	      (s2 = X0
19.06/19.37	       | ~ incident(b2, X0)
19.06/19.37	       | ~ incident(X1, X0)
19.06/19.37	       | ~ incident(X1, s2)
19.06/19.37	       | b2 = X1),
19.06/19.37	    inference('sup-', [status(thm)], ['266', '267'])).
19.06/19.37	tff('665', plain,
19.06/19.37	    ![X0]: (b2 = X0 | ~ incident(X0, s2) | ~ incident(X0, b2b3) | s2 = b2b3),
19.06/19.37	    inference('sup-', [status(thm)], ['663', '664'])).
19.06/19.37	tff('666', plain,
19.06/19.37	    ((b1 = a1 | s2 = b2b3 | ~ incident(b3, b2b3) | b2 = b3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['662', '665'])).
19.06/19.37	tff('667', plain,  incident(b3, b2b3),
19.06/19.37	    inference('cnf', [status(esa)], [ib3b2])).
19.06/19.37	tff('668', plain,
19.06/19.37	    ((b1 = a1 | s2 = b2b3 | b2 = b3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['666', '667'])).
19.06/19.37	tff('669', plain, b3 != b2,
19.06/19.37	    inference('simpl_trail', [status(thm)], ['94', '96'])).
19.06/19.37	tff('670', plain,
19.06/19.37	    ((b1 = a1 | s2 = b2b3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['668', '669'])).
19.06/19.37	tff('671', plain,  incident(a2, s2), inference('cnf', [status(esa)], [ia2s2])).
19.06/19.37	tff('672', plain,
19.06/19.37	    (( incident(a2, b2b3) | b1 = a1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['670', '671'])).
19.06/19.37	tff('673', plain,
19.06/19.37	    ![X0]: (p1 = X0 | ~ incident(X0, b2b3) | ~ incident(X0, a2a3)),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['195', '200'])).
19.06/19.37	tff('674', plain,
19.06/19.37	    ((b1 = a1 | ~ incident(a2, a2a3) | p1 = a2))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['672', '673'])).
19.06/19.37	tff('675', plain,  incident(a2, a2a3),
19.06/19.37	    inference('cnf', [status(esa)], [ia2a3])).
19.06/19.37	tff('676', plain,
19.06/19.37	    ((b1 = a1 | p1 = a2)) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['674', '675'])).
19.06/19.37	tff('677', plain,  incident(p3, a1a2),
19.06/19.37	    inference('cnf', [status(esa)], [ip3a])).
19.06/19.37	tff('678', plain, ( incident(b3, a1a2)) <= (( incident(b3, a1a2))),
19.06/19.37	    inference('split', [status(esa)], ['6'])).
19.06/19.37	tff('679', plain,
19.06/19.37	    ![X0, X1, X2]:
19.06/19.37	      (sk_C_1(X1, X0) = X2
19.06/19.37	       | ~ incident(X1, X2)
19.06/19.37	       | ~ incident(X0, X2)
19.06/19.37	       | X1 = X0
19.06/19.37	       | ~ point(X0)
19.06/19.37	       | ~ point(X1)),
19.06/19.37	    inference('simplify', [status(thm)], ['214'])).
19.06/19.37	tff('680', plain,
19.06/19.37	    (![X0]:
19.06/19.37	       (~ point(b3)
19.06/19.37	        | ~ point(X0)
19.06/19.37	        | b3 = X0
19.06/19.37	        | ~ incident(X0, a1a2)
19.06/19.37	        | sk_C_1(b3, X0) = a1a2))
19.06/19.37	      <= (( incident(b3, a1a2))),
19.06/19.37	    inference('sup-', [status(thm)], ['678', '679'])).
19.06/19.37	tff('681', plain,  incident(b3, b2b3),
19.06/19.37	    inference('cnf', [status(esa)], [ib3b2])).
19.06/19.37	tff('682', plain, ![X11, X12]: ( point(X11) | ~ incident(X11, X12)),
19.06/19.37	    inference('cnf', [status(esa)], [sort_point])).
19.06/19.37	tff('683', plain,  point(b3),
19.06/19.37	    inference('sup-', [status(thm)], ['681', '682'])).
19.06/19.37	tff('684', plain,
19.06/19.37	    (![X0]:
19.06/19.37	       (~ point(X0) | b3 = X0 | ~ incident(X0, a1a2) | sk_C_1(b3, X0) = a1a2))
19.06/19.37	      <= (( incident(b3, a1a2))),
19.06/19.37	    inference('demod', [status(thm)], ['680', '683'])).
19.06/19.37	tff('685', plain,
19.06/19.37	    ((sk_C_1(b3, p3) = a1a2 | b3 = p3 | ~ point(p3)))
19.06/19.37	      <= (( incident(b3, a1a2))),
19.06/19.37	    inference('sup-', [status(thm)], ['677', '684'])).
19.06/19.37	tff('686', plain,  point(p3),
19.06/19.37	    inference('sup-', [status(thm)], ['177', '178'])).
19.06/19.37	tff('687', plain,
19.06/19.37	    ((sk_C_1(b3, p3) = a1a2 | b3 = p3)) <= (( incident(b3, a1a2))),
19.06/19.37	    inference('demod', [status(thm)], ['685', '686'])).
19.06/19.37	tff('688', plain,
19.06/19.37	    ![X16, X17]:
19.06/19.37	      (~ point(X16) | ~ point(X17) |  incident(X16, sk_C_1(X17, X16))),
19.06/19.37	    inference('cnf', [status(esa)], [join])).
19.06/19.37	tff('689', plain,
19.06/19.37	    ![X5]: (~ incident(p3, X5) | ~ incident(p1, X5) | ~ incident(p2, X5)),
19.06/19.37	    inference('simpl_trail', [status(thm)], ['172', '174'])).
19.06/19.37	tff('690', plain,
19.06/19.37	    ![X0]:
19.06/19.37	      (~ point(X0)
19.06/19.37	       | ~ point(p3)
19.06/19.37	       | ~ incident(p2, sk_C_1(X0, p3))
19.06/19.37	       | ~ incident(p1, sk_C_1(X0, p3))),
19.06/19.37	    inference('sup-', [status(thm)], ['688', '689'])).
19.06/19.37	tff('691', plain,  point(p3),
19.06/19.37	    inference('sup-', [status(thm)], ['177', '178'])).
19.06/19.37	tff('692', plain,
19.06/19.37	    ![X0]:
19.06/19.37	      (~ point(X0)
19.06/19.37	       | ~ incident(p2, sk_C_1(X0, p3))
19.06/19.37	       | ~ incident(p1, sk_C_1(X0, p3))),
19.06/19.37	    inference('demod', [status(thm)], ['690', '691'])).
19.06/19.37	tff('693', plain,
19.06/19.37	    ((~ incident(p2, a1a2)
19.06/19.37	      | b3 = p3
19.06/19.37	      | ~ incident(p1, sk_C_1(b3, p3))
19.06/19.37	      | ~ point(b3))) <= (( incident(b3, a1a2))),
19.06/19.37	    inference('sup-', [status(thm)], ['687', '692'])).
19.06/19.37	tff('694', plain,  point(b3),
19.06/19.37	    inference('sup-', [status(thm)], ['681', '682'])).
19.06/19.37	tff('695', plain,
19.06/19.37	    ((~ incident(p2, a1a2) | b3 = p3 | ~ incident(p1, sk_C_1(b3, p3))))
19.06/19.37	      <= (( incident(b3, a1a2))),
19.06/19.37	    inference('demod', [status(thm)], ['693', '694'])).
19.06/19.37	tff('696', plain,
19.06/19.37	    ((~ incident(a2, sk_C_1(b3, p3))
19.06/19.37	      | b1 = a1
19.06/19.37	      | b3 = p3
19.06/19.37	      | ~ incident(p2, a1a2)))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['676', '695'])).
19.06/19.37	tff('697', plain,
19.06/19.37	    (b1 = p3) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['629', '630'])).
19.06/19.37	tff('698', plain,
19.06/19.37	    (b1 = p3) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['629', '630'])).
19.06/19.37	tff('699', plain,
19.06/19.37	    ((sk_C_1(b3, p3) = a1a2 | b3 = p3)) <= (( incident(b3, a1a2))),
19.06/19.37	    inference('demod', [status(thm)], ['685', '686'])).
19.06/19.37	tff('700', plain,
19.06/19.37	    ((sk_C_1(b3, b1) = a1a2 | b3 = p3))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['698', '699'])).
19.06/19.37	tff('701', plain,
19.06/19.37	    (b1 = p3) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['629', '630'])).
19.06/19.37	tff('702', plain,
19.06/19.37	    ((sk_C_1(b3, b1) = a1a2 | b3 = b1))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['700', '701'])).
19.06/19.37	tff('703', plain, b1 != b3, inference('clc', [status(thm)], ['141', '142'])).
19.06/19.37	tff('704', plain,
19.06/19.37	    (sk_C_1(b3, b1) = a1a2)
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['702', '703'])).
19.06/19.37	tff('705', plain,  incident(a2, a1a2),
19.06/19.37	    inference('cnf', [status(esa)], [ia2a1])).
19.06/19.37	tff('706', plain,
19.06/19.37	    (b1 = p3) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['629', '630'])).
19.06/19.37	tff('707', plain,
19.06/19.37	    (a1a2 = b3b1) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['617'])).
19.06/19.37	tff('708', plain,  incident(p2, b3b1),
19.06/19.37	    inference('cnf', [status(esa)], [ip2b])).
19.06/19.37	tff('709', plain,
19.06/19.37	    ( incident(p2, a1a2)) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['707', '708'])).
19.06/19.37	tff('710', plain,  incident(p2, a3a1),
19.06/19.37	    inference('cnf', [status(esa)], [ip2a])).
19.06/19.37	tff('711', plain,  incident(a1, a1a2),
19.06/19.37	    inference('cnf', [status(esa)], [ia1a2])).
19.06/19.37	tff('712', plain,
19.06/19.37	    ![X0, X1]:
19.06/19.37	      (a3a1 = X0
19.06/19.37	       | ~ incident(a1, X0)
19.06/19.37	       | ~ incident(X1, X0)
19.06/19.37	       | ~ incident(X1, a3a1)
19.06/19.37	       | a1 = X1),
19.06/19.37	    inference('sup-', [status(thm)], ['113', '114'])).
19.06/19.37	tff('713', plain,
19.06/19.37	    ![X0]:
19.06/19.37	      (a1 = X0 | ~ incident(X0, a3a1) | ~ incident(X0, a1a2) | a3a1 = a1a2),
19.06/19.37	    inference('sup-', [status(thm)], ['711', '712'])).
19.06/19.37	tff('714', plain, (a3a1 = a1a2 | ~ incident(p2, a1a2) | a1 = p2),
19.06/19.37	    inference('sup-', [status(thm)], ['710', '713'])).
19.06/19.37	tff('715', plain,
19.06/19.37	    ((a1 = p2 | a3a1 = a1a2))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['709', '714'])).
19.06/19.37	tff('716', plain,
19.06/19.37	    (a1a2 != a3a1) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['657', '658'])).
19.06/19.37	tff('717', plain,
19.06/19.37	    (a1 = p2) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['715', '716'])).
19.06/19.37	tff('718', plain,  incident(a1, a1a2),
19.06/19.37	    inference('cnf', [status(esa)], [ia1a2])).
19.06/19.37	tff('719', plain,
19.06/19.37	    ((b1 = a1 | b3 = b1)) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)],
19.06/19.37	              ['696', '697', '704', '705', '706', '717', '718'])).
19.06/19.37	tff('720', plain, b1 != b3, inference('clc', [status(thm)], ['141', '142'])).
19.06/19.37	tff('721', plain,
19.06/19.37	    (b1 = a1) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['719', '720'])).
19.06/19.37	tff('722', plain,
19.06/19.37	    (a1 = p3) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['631', '721'])).
19.06/19.37	tff('723', plain,
19.06/19.37	    ![X5]: (~ incident(p3, X5) | ~ incident(p1, X5) | ~ incident(p2, X5)),
19.06/19.37	    inference('simpl_trail', [status(thm)], ['172', '174'])).
19.06/19.37	tff('724', plain,
19.06/19.37	    (![X0]: (~ incident(a1, X0) | ~ incident(p2, X0) | ~ incident(p1, X0)))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['722', '723'])).
19.06/19.37	tff('725', plain,
19.06/19.37	    (a1 = p2) <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['715', '716'])).
19.06/19.37	tff('726', plain,
19.06/19.37	    (![X0]: (~ incident(a1, X0) | ~ incident(a1, X0) | ~ incident(p1, X0)))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['724', '725'])).
19.06/19.37	tff('727', plain,
19.06/19.37	    (![X0]: (~ incident(p1, X0) | ~ incident(a1, X0)))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('simplify', [status(thm)], ['726'])).
19.06/19.37	tff('728', plain,
19.06/19.37	    (![X0]: (~ point(p1) | ~ point(X0) | ~ incident(a1, sk_C_1(p1, X0))))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['566', '727'])).
19.06/19.37	tff('729', plain,  incident(p1, b2b3),
19.06/19.37	    inference('cnf', [status(esa)], [ip1b])).
19.06/19.37	tff('730', plain, ![X11, X12]: ( point(X11) | ~ incident(X11, X12)),
19.06/19.37	    inference('cnf', [status(esa)], [sort_point])).
19.06/19.37	tff('731', plain,  point(p1),
19.06/19.37	    inference('sup-', [status(thm)], ['729', '730'])).
19.06/19.37	tff('732', plain,
19.06/19.37	    (![X0]: (~ point(X0) | ~ incident(a1, sk_C_1(p1, X0))))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('demod', [status(thm)], ['728', '731'])).
19.06/19.37	tff('733', plain,
19.06/19.37	    ((~ point(p1) | ~ point(a1) | ~ point(a1)))
19.06/19.37	      <= (( incident(b3, a1a2)) & ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['565', '732'])).
19.06/19.37	tff('734', plain,  point(p1),
19.06/19.37	    inference('sup-', [status(thm)], ['729', '730'])).
19.06/19.37	tff('735', plain,  incident(a1, a3a1),
19.06/19.37	    inference('cnf', [status(esa)], [ia1a3])).
19.06/19.37	tff('736', plain, ![X11, X12]: ( point(X11) | ~ incident(X11, X12)),
19.06/19.37	    inference('cnf', [status(esa)], [sort_point])).
19.06/19.37	tff('737', plain,  point(a1),
19.06/19.37	    inference('sup-', [status(thm)], ['735', '736'])).
19.06/19.37	tff('738', plain,  point(a1),
19.06/19.37	    inference('sup-', [status(thm)], ['735', '736'])).
19.06/19.37	tff('739', plain, ~ ( incident(b3, a1a2)) | ~ ( incident(a2, b3b1)),
19.06/19.37	    inference('demod', [status(thm)], ['733', '734', '737', '738'])).
19.06/19.37	tff('740', plain, ( incident(a1, b2b3)) | ( incident(b3, a1a2)),
19.06/19.37	    inference('split', [status(esa)], ['6'])).
19.06/19.37	tff('741', plain,
19.06/19.37	    ( incident(a3, b3b1)) <= (( incident(b2, a3a1)) & ( incident(a1, b2b3))),
19.06/19.37	    inference('sup+', [status(thm)], ['230', '231'])).
19.06/19.37	tff('742', plain,
19.06/19.37	    ((a2a3 = b3b1 | ~ incident(a3, b3b1))) <= (( incident(a2, b3b1))),
19.06/19.37	    inference('simplify_reflect-', [status(thm)], ['305', '308'])).
19.06/19.37	tff('743', plain,
19.06/19.37	    (a2a3 = b3b1)
19.06/19.37	      <= (( incident(b2, a3a1)) & 
19.06/19.37	          ( incident(a1, b2b3)) & 
19.06/19.37	          ( incident(a2, b3b1))),
19.06/19.37	    inference('sup-', [status(thm)], ['741', '742'])).
19.06/19.37	tff('744', plain,  incident(b1, b3b1),
19.06/19.37	    inference('cnf', [status(esa)], [ib1b3])).
19.06/19.37	tff('745', plain,
19.06/19.37	    ( incident(b1, a2a3))
19.06/19.37	      <= (( incident(b2, a3a1)) & 
19.06/19.37	          ( incident(a1, b2b3)) & 
19.06/19.37	          ( incident(a2, b3b1))),
19.06/19.37	    inference('sup+', [status(thm)], ['743', '744'])).
19.06/19.37	tff('746', plain, (~ incident(b1, a2a3)) <= (~ ( incident(b1, a2a3))),
19.06/19.37	    inference('split', [status(esa)], ['250'])).
19.06/19.37	tff('747', plain,
19.06/19.37	    ~ ( incident(b2, a3a1)) | ~ ( incident(a1, b2b3)) | 
19.06/19.37	    ~ ( incident(a2, b3b1)) | ( incident(b1, a2a3)),
19.06/19.37	    inference('sup-', [status(thm)], ['745', '746'])).
19.06/19.37	tff('748', plain, ( incident(b2, a3a1)) | ( incident(a3, b1b2)),
19.17/19.37	    inference('split', [status(esa)], ['2'])).
19.17/19.37	tff('749', plain, $false,
19.17/19.37	    inference('sat_resolution*', [status(thm)],
19.17/19.37	              ['1', '249', '251', '29', '418', '563', '564', '739', '740', 
19.17/19.37	               '747', '748'])).
19.17/19.37	
19.17/19.37	% SZS output end Refutation
19.17/19.37	
19.17/19.37	% Zipperpin 1.5 exiting
19.17/19.37	EOF