0.00/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.10	% Command    : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.aHAYhrhQuh
0.09/0.31	% Computer   : n008.cluster.edu
0.09/0.31	% Model      : x86_64 x86_64
0.09/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.31	% Memory     : 8042.1875MB
0.09/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.09/0.31	% CPULimit   : 960
0.09/0.31	% DateTime   : Thu Jul  2 06:50:44 EDT 2020
0.09/0.31	% CPUTime    : 
0.09/0.31	% Running portfolio for 120 s
0.09/0.31	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.09/0.31	% Number of cores: 8
0.09/0.31	% Python version: Python 3.6.8
0.16/0.31	% Running in FO mode
86.84/87.43	% Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25
86.84/87.43	% Warning:
86.84/87.43	% To remain in the chosen logic fragment, unification with booleans has been disabled.
86.84/87.43	% 
86.84/87.43	% Running /export/starexec/sandbox2/solver/bin/fo/fo8.sh for 20
86.84/87.43	% Warning:
86.84/87.43	% To remain in the chosen logic fragment, unification with booleans has been disabled.
86.84/87.43	% 
86.84/87.43	% Running /export/starexec/sandbox2/solver/bin/fo/fo5.sh for 20
86.84/87.43	% Warning:
86.84/87.43	% To remain in the chosen logic fragment, unification with booleans has been disabled.
86.84/87.43	% 
86.84/87.43	% Running /export/starexec/sandbox2/solver/bin/fo/fo11.sh for 20
86.84/87.43	% Warning:
86.84/87.43	% To remain in the chosen logic fragment, unification with booleans has been disabled.
86.84/87.43	% 
86.84/87.43	% Running /export/starexec/sandbox2/solver/bin/fo/fo11.lcnf.sh for 15
86.84/87.43	% Solved by: fo/fo11.lcnf.sh
86.84/87.43	To remain in the chosen logic fragment, unification with booleans has been disabled.
86.84/87.43	% done 8294 iterations in 1.937s
86.84/87.43	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
86.84/87.43	% SZS output start Refutation
86.84/87.43	tff(nc3, conjecture,
86.84/87.43	  (((~
86.84/87.43	      (?[A]:
86.84/87.43	         (![B]:
86.84/87.43	            ((g_false_only(B,A) & 
86.84/87.43	              (?[C]: (g_true_only(B,C) & g_true_only(C,B)))) | 
86.84/87.43	             ((![C]: (g_false_only(C,B) | g_false_only(B,C))) & 
86.84/87.43	              g_true_only(B,A)))))) & 
86.84/87.43	    (?[A]:
86.84/87.43	       ((?[B]:
86.84/87.43	           ((~(?[C]: (g_true_only(B,C) & g_true_only(C,B)))) & 
86.84/87.43	            (?[C]:
86.84/87.43	               ((g_both(B,C) | g_both(C,B)) & (~g_false_only(C,B)) & 
86.84/87.43	                (~g_false_only(B,C)))) & 
86.84/87.43	            g_both(B,A))) & 
86.84/87.43	        (~
86.84/87.43	          (?[B]:
86.84/87.43	             ((((![C]: (g_false_only(B,C) | g_false_only(C,B))) | 
86.84/87.43	                (?[C]: (g_true_only(B,C) & g_true_only(C,B)))) & 
86.84/87.43	               g_both(B,A)) | 
86.84/87.43	              (g_false_only(B,A) & 
86.84/87.43	               (((?[C]:
86.84/87.43	                    ((~g_false_only(B,C)) & (~g_false_only(C,B)) & 
86.84/87.43	                     (g_both(C,B) | g_both(B,C)))) & 
86.84/87.43	                 (~(?[C]: (g_true_only(C,B) & g_true_only(B,C))))) | 
86.84/87.43	                (![C]: (g_false_only(C,B) | g_false_only(B,C))))) | 
86.84/87.43	              ((((?[C]:
86.84/87.43	                    ((~g_false_only(B,C)) & (~g_false_only(C,B)) & 
86.84/87.43	                     (g_both(C,B) | g_both(B,C)))) & 
86.84/87.43	                 (~(?[C]: (g_true_only(C,B) & g_true_only(B,C))))) | 
86.84/87.43	                (?[C]: (g_true_only(B,C) & g_true_only(C,B)))) & 
86.84/87.43	               g_true_only(B,A)))))))) | 
86.84/87.43	   (![A]:
86.84/87.43	      (?[B]:
86.84/87.43	         ((g_true_only(B,A) & 
86.84/87.43	           ((?[C]: (g_true_only(C,B) & g_true_only(B,C))) | 
86.84/87.43	            ((~(?[C]: (g_true_only(C,B) & g_true_only(B,C)))) & 
86.84/87.43	             (?[C]:
86.84/87.43	                ((~g_false_only(C,B)) & (~g_false_only(B,C)) & 
86.84/87.43	                 (g_both(C,B) | g_both(B,C))))))) | 
86.84/87.43	          (g_false_only(B,A) & 
86.84/87.43	           ((![C]: (g_false_only(B,C) | g_false_only(C,B))) | 
86.84/87.43	            ((?[C]:
86.84/87.43	                ((~g_false_only(B,C)) & (~g_false_only(C,B)) & 
86.84/87.43	                 (g_both(B,C) | g_both(C,B)))) & 
86.84/87.43	             (~(?[C]: (g_true_only(C,B) & g_true_only(B,C))))))) | 
86.84/87.43	          (g_both(B,A) & 
86.84/87.43	           ((?[C]: (g_true_only(C,B) & g_true_only(B,C))) | 
86.84/87.43	            (![C]: (g_false_only(C,B) | g_false_only(B,C)))))))))).
86.84/87.43	tff(zf_stmt_0, negated_conjecture,
86.84/87.43	  (~
86.84/87.43	    (((~
86.84/87.43	        (?[A]:
86.84/87.43	           (![B]:
86.84/87.43	              ((g_false_only(B,A) & 
86.84/87.43	                (?[C]: (g_true_only(B,C) & g_true_only(C,B)))) | 
86.84/87.43	               ((![C]: (g_false_only(C,B) | g_false_only(B,C))) & 
86.84/87.43	                g_true_only(B,A)))))) & 
86.84/87.43	      (?[A]:
86.84/87.43	         ((?[B]:
86.84/87.43	             ((~(?[C]: (g_true_only(B,C) & g_true_only(C,B)))) & 
86.84/87.43	              (?[C]:
86.84/87.43	                 ((g_both(B,C) | g_both(C,B)) & (~g_false_only(C,B)) & 
86.84/87.43	                  (~g_false_only(B,C)))) & 
86.84/87.43	              g_both(B,A))) & 
86.84/87.43	          (~
86.84/87.43	            (?[B]:
86.84/87.43	               ((((![C]: (g_false_only(B,C) | g_false_only(C,B))) | 
86.84/87.43	                  (?[C]: (g_true_only(B,C) & g_true_only(C,B)))) & 
86.84/87.43	                 g_both(B,A)) | 
86.84/87.43	                (g_false_only(B,A) & 
86.84/87.43	                 (((?[C]:
86.84/87.43	                      ((~g_false_only(B,C)) & (~g_false_only(C,B)) & 
86.84/87.43	                       (g_both(C,B) | g_both(B,C)))) & 
86.84/87.43	                   (~(?[C]: (g_true_only(C,B) & g_true_only(B,C))))) | 
86.84/87.43	                  (![C]: (g_false_only(C,B) | g_false_only(B,C))))) | 
86.84/87.43	                ((((?[C]:
86.84/87.43	                      ((~g_false_only(B,C)) & (~g_false_only(C,B)) & 
86.84/87.43	                       (g_both(C,B) | g_both(B,C)))) & 
86.84/87.43	                   (~(?[C]: (g_true_only(C,B) & g_true_only(B,C))))) | 
86.84/87.43	                  (?[C]: (g_true_only(B,C) & g_true_only(C,B)))) & 
86.84/87.43	                 g_true_only(B,A)))))))) | 
86.84/87.43	     (![A]:
86.84/87.43	        (?[B]:
86.84/87.43	           ((g_true_only(B,A) & 
86.84/87.43	             ((?[C]: (g_true_only(C,B) & g_true_only(B,C))) | 
86.84/87.43	              ((~(?[C]: (g_true_only(C,B) & g_true_only(B,C)))) & 
86.84/87.43	               (?[C]:
86.84/87.43	                  ((~g_false_only(C,B)) & (~g_false_only(B,C)) & 
86.84/87.43	                   (g_both(C,B) | g_both(B,C))))))) | 
86.84/87.43	            (g_false_only(B,A) & 
86.84/87.43	             ((![C]: (g_false_only(B,C) | g_false_only(C,B))) | 
86.84/87.43	              ((?[C]:
86.84/87.43	                  ((~g_false_only(B,C)) & (~g_false_only(C,B)) & 
86.84/87.43	                   (g_both(B,C) | g_both(C,B)))) & 
86.84/87.43	               (~(?[C]: (g_true_only(C,B) & g_true_only(B,C))))))) | 
86.84/87.43	            (g_both(B,A) & 
86.84/87.43	             ((?[C]: (g_true_only(C,B) & g_true_only(B,C))) | 
86.84/87.43	              (![C]: (g_false_only(C,B) | g_false_only(B,C))))))))))).
86.84/87.43	tff('0', plain,
86.84/87.43	    ~ (((~((??((^[Y0 : $i]:
86.84/87.43	                  (!!((^[Y1 : $i]:
86.84/87.43	                         ((g_false_only(Y1, Y0) &
86.84/87.43	                           (??((^[Y2 : $i]:
86.84/87.43	                                  (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                          ((!!((^[Y2 : $i]:
86.84/87.43	                                  (g_false_only(Y2, Y1) |
86.84/87.43	                                   g_false_only(Y1, Y2))))) &
86.84/87.43	                           g_true_only(Y1, Y0))))))))))) &
86.84/87.43	        (??((^[Y0 : $i]:
86.84/87.43	               ((??((^[Y1 : $i]:
86.84/87.43	                       ((~((??((^[Y2 : $i]:
86.84/87.43	                                  (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))))&
86.84/87.43	                        (??((^[Y2 : $i]:
86.84/87.43	                               ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                        g_both(Y1, Y0))))) &
86.84/87.43	                (~((??((^[Y1 : $i]:
86.84/87.43	                          ((((!!((^[Y2 : $i]:
86.84/87.43	                                    (g_false_only(Y1, Y2) |
86.84/87.43	                                     g_false_only(Y2, Y1))))) |
86.84/87.43	                             (??((^[Y2 : $i]:
86.84/87.43	                                    (g_true_only(Y1, Y2) &
86.84/87.43	                                     g_true_only(Y2, Y1)))))) &
86.84/87.43	                            g_both(Y1, Y0))|
86.84/87.43	                           (g_false_only(Y1, Y0) &
86.84/87.43	                            (((??((^[Y2 : $i]:
86.84/87.43	                                     ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                      (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                      (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                              (~((??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y2, Y1) &
86.84/87.43	                                         g_true_only(Y1, Y2)))))))) |
86.84/87.43	                             (!!((^[Y2 : $i]:
86.84/87.43	                                    (g_false_only(Y2, Y1) |
86.84/87.43	                                     g_false_only(Y1, Y2)))))))|
86.84/87.43	                           ((((??((^[Y2 : $i]:
86.84/87.43	                                     ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                      (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                      (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                              (~((??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y2, Y1) &
86.84/87.43	                                         g_true_only(Y1, Y2)))))))) |
86.84/87.43	                             (??((^[Y2 : $i]:
86.84/87.43	                                    (g_true_only(Y1, Y2) &
86.84/87.43	                                     g_true_only(Y2, Y1)))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))))) |
86.84/87.43	       (!!((^[Y0 : $i]:
86.84/87.43	              (??((^[Y1 : $i]:
86.84/87.43	                     ((g_true_only(Y1, Y0) &
86.84/87.43	                       ((??((^[Y2 : $i]:
86.84/87.43	                               (g_true_only(Y2, Y1) & g_true_only(Y1, Y2))))) |
86.84/87.43	                        ((~((??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y2, Y1) & g_true_only(Y1, Y2))))))) &
86.84/87.43	                         (??((^[Y2 : $i]:
86.84/87.43	                                ((~(g_false_only(Y2, Y1)))&
86.84/87.43	                                 (~(g_false_only(Y1, Y2)))&
86.84/87.43	                                 (g_both(Y2, Y1) | g_both(Y1, Y2)))))))))|
86.84/87.43	                      (g_false_only(Y1, Y0) &
86.84/87.43	                       ((!!((^[Y2 : $i]:
86.84/87.43	                               (g_false_only(Y1, Y2) | g_false_only(Y2, Y1))))) |
86.84/87.43	                        ((??((^[Y2 : $i]:
86.84/87.43	                                ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                 (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                 (g_both(Y1, Y2) | g_both(Y2, Y1)))))) &
86.84/87.43	                         (~((??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y2, Y1) & g_true_only(Y1, Y2))))))))))|
86.84/87.43	                      (g_both(Y1, Y0) &
86.84/87.43	                       ((??((^[Y2 : $i]:
86.84/87.43	                               (g_true_only(Y2, Y1) & g_true_only(Y1, Y2))))) |
86.84/87.43	                        (!!((^[Y2 : $i]:
86.84/87.43	                               (g_false_only(Y2, Y1) | g_false_only(Y1, Y2))))))))))))))),
86.84/87.43	    inference('cnf', [status(esa)], [zf_stmt_0])).
86.84/87.43	tff('1', plain,
86.84/87.43	    ~ ((~((??((^[Y0 : $i]:
86.84/87.43	                 (!!((^[Y1 : $i]:
86.84/87.43	                        ((g_false_only(Y1, Y0) &
86.84/87.43	                          (??((^[Y2 : $i]:
86.84/87.43	                                 (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                         ((!!((^[Y2 : $i]:
86.84/87.43	                                 (g_false_only(Y2, Y1) | g_false_only(Y1, Y2))))) &
86.84/87.43	                          g_true_only(Y1, Y0))))))))))) &
86.84/87.43	       (??((^[Y0 : $i]:
86.84/87.43	              ((??((^[Y1 : $i]:
86.84/87.43	                      ((~((??((^[Y2 : $i]:
86.84/87.43	                                 (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))))&
86.84/87.43	                       (??((^[Y2 : $i]:
86.84/87.43	                              ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                               (~(g_false_only(Y2, Y1)))&
86.84/87.43	                               (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                       g_both(Y1, Y0))))) &
86.84/87.43	               (~((??((^[Y1 : $i]:
86.84/87.43	                         ((((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y1, Y2) |
86.84/87.43	                                    g_false_only(Y2, Y1))))) |
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) &
86.84/87.43	                           g_both(Y1, Y0))|
86.84/87.43	                          (g_false_only(Y1, Y0) &
86.84/87.43	                           (((??((^[Y2 : $i]:
86.84/87.43	                                    ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                     (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                     (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                             (~((??((^[Y2 : $i]:
86.84/87.43	                                       (g_true_only(Y2, Y1) &
86.84/87.43	                                        g_true_only(Y1, Y2)))))))) |
86.84/87.43	                            (!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2)))))))|
86.84/87.43	                          ((((??((^[Y2 : $i]:
86.84/87.43	                                    ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                     (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                     (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                             (~((??((^[Y2 : $i]:
86.84/87.43	                                       (g_true_only(Y2, Y1) &
86.84/87.43	                                        g_true_only(Y1, Y2)))))))) |
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) &
86.84/87.43	                           g_true_only(Y1, Y0))))))))))))),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['0'])).
86.84/87.43	tff('2', plain,
86.84/87.43	    ( (??((^[Y0 : $i]:
86.84/87.43	             (!!((^[Y1 : $i]:
86.84/87.43	                    ((g_false_only(Y1, Y0) &
86.84/87.43	                      (??((^[Y2 : $i]:
86.84/87.43	                             (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                     ((!!((^[Y2 : $i]:
86.84/87.43	                             (g_false_only(Y2, Y1) | g_false_only(Y1, Y2))))) &
86.84/87.43	                      g_true_only(Y1, Y0)))))))))
86.84/87.43	     | ~ (??((^[Y0 : $i]:
86.84/87.43	                ((??((^[Y1 : $i]:
86.84/87.43	                        ((~((??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))))&
86.84/87.43	                         (??((^[Y2 : $i]:
86.84/87.43	                                ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                 (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                 (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                         g_both(Y1, Y0))))) &
86.84/87.43	                 (~((??((^[Y1 : $i]:
86.84/87.43	                           ((((!!((^[Y2 : $i]:
86.84/87.43	                                     (g_false_only(Y1, Y2) |
86.84/87.43	                                      g_false_only(Y2, Y1))))) |
86.84/87.43	                              (??((^[Y2 : $i]:
86.84/87.43	                                     (g_true_only(Y1, Y2) &
86.84/87.43	                                      g_true_only(Y2, Y1)))))) &
86.84/87.43	                             g_both(Y1, Y0))|
86.84/87.43	                            (g_false_only(Y1, Y0) &
86.84/87.43	                             (((??((^[Y2 : $i]:
86.84/87.43	                                      ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                       (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                       (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                               (~((??((^[Y2 : $i]:
86.84/87.43	                                         (g_true_only(Y2, Y1) &
86.84/87.43	                                          g_true_only(Y1, Y2)))))))) |
86.84/87.43	                              (!!((^[Y2 : $i]:
86.84/87.43	                                     (g_false_only(Y2, Y1) |
86.84/87.43	                                      g_false_only(Y1, Y2)))))))|
86.84/87.43	                            ((((??((^[Y2 : $i]:
86.84/87.43	                                      ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                       (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                       (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                               (~((??((^[Y2 : $i]:
86.84/87.43	                                         (g_true_only(Y2, Y1) &
86.84/87.43	                                          g_true_only(Y1, Y2)))))))) |
86.84/87.43	                              (??((^[Y2 : $i]:
86.84/87.43	                                     (g_true_only(Y1, Y2) &
86.84/87.43	                                      g_true_only(Y2, Y1)))))) &
86.84/87.43	                             g_true_only(Y1, Y0))))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['1'])).
86.84/87.43	tff('3', plain,
86.84/87.43	    ( (??((^[Y0 : $i]:
86.84/87.43	             (!!((^[Y1 : $i]:
86.84/87.43	                    ((g_false_only(Y1, Y0) &
86.84/87.43	                      (??((^[Y2 : $i]:
86.84/87.43	                             (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                     ((!!((^[Y2 : $i]:
86.84/87.43	                             (g_false_only(Y2, Y1) | g_false_only(Y1, Y2))))) &
86.84/87.43	                      g_true_only(Y1, Y0))))))))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('split', [status(esa)], ['2'])).
86.84/87.43	tff('4', plain,
86.84/87.43	    ( (!!((^[Y0 : $i]:
86.84/87.43	             ((g_false_only(Y0, '#sk2') &
86.84/87.43	               (??((^[Y1 : $i]: (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) |
86.84/87.43	              ((!!((^[Y1 : $i]: (g_false_only(Y1, Y0) | g_false_only(Y0, Y1))))) &
86.84/87.43	               g_true_only(Y0, '#sk2')))))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_exists', [status(thm)], ['3'])).
86.84/87.43	tff('5', plain,
86.84/87.43	    (![X1]:
86.84/87.43	        ((g_false_only(X1, '#sk2') &
86.84/87.43	          (??((^[Y0 : $i]: (g_true_only(X1, Y0) & g_true_only(Y0, X1)))))) |
86.84/87.43	         ((!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0))))) &
86.84/87.43	          g_true_only(X1, '#sk2'))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['4'])).
86.84/87.43	tff('6', plain,
86.84/87.43	    (![X1]:
86.84/87.43	       ( (g_false_only(X1, '#sk2') &
86.84/87.43	          (??((^[Y0 : $i]: (g_true_only(X1, Y0) & g_true_only(Y0, X1))))))
86.84/87.43	        |  ((!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0))))) &
86.84/87.43	            g_true_only(X1, '#sk2'))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['5'])).
86.84/87.43	tff('7', plain,
86.84/87.43	    (![X1]:
86.84/87.43	       ( (??((^[Y0 : $i]: (g_true_only(X1, Y0) & g_true_only(Y0, X1)))))
86.84/87.43	        |  ((!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0))))) &
86.84/87.43	            g_true_only(X1, '#sk2'))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['6'])).
86.84/87.43	tff('8', plain,
86.84/87.43	    (![X1]:
86.84/87.43	       ( (g_true_only(X1, '#sk4'(X1)) & g_true_only('#sk4'(X1), X1))
86.84/87.43	        |  ((!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0))))) &
86.84/87.43	            g_true_only(X1, '#sk2'))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_exists', [status(thm)], ['7'])).
86.84/87.43	tff('9', plain,
86.84/87.43	    (![X1]:
86.84/87.43	       ( g_true_only(X1, '#sk4'(X1))
86.84/87.43	        |  ((!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0))))) &
86.84/87.43	            g_true_only(X1, '#sk2'))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['8'])).
86.84/87.43	tff('10', plain,
86.84/87.43	    (![X1]:
86.84/87.43	       ( (!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0)))))
86.84/87.43	        |  g_true_only(X1, '#sk4'(X1))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['9'])).
86.84/87.43	tff('11', plain,
86.84/87.43	    (![X1, X2]:
86.84/87.43	       ( (g_false_only(X2, X1) | g_false_only(X1, X2))
86.84/87.43	        |  g_true_only(X1, '#sk4'(X1))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['10'])).
86.84/87.43	tff('12', plain,
86.84/87.43	    (![X1, X2]:
86.84/87.43	       ( g_false_only(X2, X1)
86.84/87.43	        |  g_false_only(X1, X2)
86.84/87.43	        |  g_true_only(X1, '#sk4'(X1))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['11'])).
86.84/87.43	tff(exhaustion_g, axiom,
86.84/87.43	  (![X_2,X_1]:
86.84/87.43	     (g_true_only(X_2,X_1) | g_both(X_2,X_1) | g_false_only(X_2,X_1)))).
86.84/87.43	tff('13', plain,
86.84/87.43	     (!!((^[Y0 : $i]:
86.84/87.43	            (!!((^[Y1 : $i]:
86.84/87.43	                   (g_true_only(Y0, Y1)|g_both(Y0, Y1)|g_false_only(Y0, Y1)))))))),
86.84/87.43	    inference('cnf', [status(esa)], [exhaustion_g])).
86.84/87.43	tff('14', plain,
86.84/87.43	    ![X1]:
86.84/87.43	       (!!((^[Y0 : $i]:
86.84/87.43	              (g_true_only(X1, Y0)|g_both(X1, Y0)|g_false_only(X1, Y0))))),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['13'])).
86.84/87.43	tff('15', plain,
86.84/87.43	    ![X1, X2]:  (g_true_only(X1, X2)|g_both(X1, X2)|g_false_only(X1, X2)),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['14'])).
86.84/87.43	tff('16', plain,
86.84/87.43	    ![X1, X2]:
86.84/87.43	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.43	tff('17', plain,
86.84/87.43	    ![X1, X2]:
86.84/87.43	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.43	tff('18', plain,
86.84/87.43	    (![X1]:
86.84/87.43	       ( g_false_only(X1, '#sk2')
86.84/87.43	        |  ((!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0))))) &
86.84/87.43	            g_true_only(X1, '#sk2'))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['6'])).
86.84/87.43	tff('19', plain,
86.84/87.43	    (![X1]: ( g_true_only(X1, '#sk2') |  g_false_only(X1, '#sk2')))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['18'])).
86.84/87.43	tff('20', plain,
86.84/87.43	    ~ (!!((^[Y0 : $i]:
86.84/87.43	             (??((^[Y1 : $i]:
86.84/87.43	                    ((g_true_only(Y1, Y0) &
86.84/87.43	                      ((??((^[Y2 : $i]:
86.84/87.43	                              (g_true_only(Y2, Y1) & g_true_only(Y1, Y2))))) |
86.84/87.43	                       ((~((??((^[Y2 : $i]:
86.84/87.43	                                  (g_true_only(Y2, Y1) & g_true_only(Y1, Y2))))))) &
86.84/87.43	                        (??((^[Y2 : $i]:
86.84/87.43	                               ((~(g_false_only(Y2, Y1)))&
86.84/87.43	                                (~(g_false_only(Y1, Y2)))&
86.84/87.43	                                (g_both(Y2, Y1) | g_both(Y1, Y2)))))))))|
86.84/87.43	                     (g_false_only(Y1, Y0) &
86.84/87.43	                      ((!!((^[Y2 : $i]:
86.84/87.43	                              (g_false_only(Y1, Y2) | g_false_only(Y2, Y1))))) |
86.84/87.43	                       ((??((^[Y2 : $i]:
86.84/87.43	                               ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                (g_both(Y1, Y2) | g_both(Y2, Y1)))))) &
86.84/87.43	                        (~((??((^[Y2 : $i]:
86.84/87.43	                                  (g_true_only(Y2, Y1) & g_true_only(Y1, Y2))))))))))|
86.84/87.43	                     (g_both(Y1, Y0) &
86.84/87.43	                      ((??((^[Y2 : $i]:
86.84/87.43	                              (g_true_only(Y2, Y1) & g_true_only(Y1, Y2))))) |
86.84/87.43	                       (!!((^[Y2 : $i]:
86.84/87.43	                              (g_false_only(Y2, Y1) | g_false_only(Y1, Y2)))))))))))))),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['0'])).
86.84/87.43	tff('21', plain,
86.84/87.43	    ~ (??((^[Y0 : $i]:
86.84/87.43	             ((g_true_only(Y0, '#sk1') &
86.84/87.43	               ((??((^[Y1 : $i]: (g_true_only(Y1, Y0) & g_true_only(Y0, Y1))))) |
86.84/87.43	                ((~((??((^[Y1 : $i]:
86.84/87.43	                           (g_true_only(Y1, Y0) & g_true_only(Y0, Y1))))))) &
86.84/87.43	                 (??((^[Y1 : $i]:
86.84/87.43	                        ((~(g_false_only(Y1, Y0)))&(~(g_false_only(Y0, Y1)))&
86.84/87.43	                         (g_both(Y1, Y0) | g_both(Y0, Y1)))))))))|
86.84/87.43	              (g_false_only(Y0, '#sk1') &
86.84/87.43	               ((!!((^[Y1 : $i]:
86.84/87.43	                       (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                ((??((^[Y1 : $i]:
86.84/87.43	                        ((~(g_false_only(Y0, Y1)))&(~(g_false_only(Y1, Y0)))&
86.84/87.43	                         (g_both(Y0, Y1) | g_both(Y1, Y0)))))) &
86.84/87.43	                 (~((??((^[Y1 : $i]:
86.84/87.43	                           (g_true_only(Y1, Y0) & g_true_only(Y0, Y1))))))))))|
86.84/87.43	              (g_both(Y0, '#sk1') &
86.84/87.43	               ((??((^[Y1 : $i]: (g_true_only(Y1, Y0) & g_true_only(Y0, Y1))))) |
86.84/87.43	                (!!((^[Y1 : $i]:
86.84/87.43	                       (g_false_only(Y1, Y0) | g_false_only(Y0, Y1))))))))))),
86.84/87.43	    inference('lazy_cnf_exists', [status(thm)], ['20'])).
86.84/87.43	tff('22', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      ~ ((g_true_only(X1, '#sk1') &
86.84/87.43	          ((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))) |
86.84/87.43	           ((~((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))))) &
86.84/87.43	            (??((^[Y0 : $i]:
86.84/87.43	                   ((~(g_false_only(Y0, X1)))&(~(g_false_only(X1, Y0)))&
86.84/87.43	                    (g_both(Y0, X1) | g_both(X1, Y0)))))))))|
86.84/87.43	         (g_false_only(X1, '#sk1') &
86.84/87.43	          ((!!((^[Y0 : $i]: (g_false_only(X1, Y0) | g_false_only(Y0, X1))))) |
86.84/87.43	           ((??((^[Y0 : $i]:
86.84/87.43	                   ((~(g_false_only(X1, Y0)))&(~(g_false_only(Y0, X1)))&
86.84/87.43	                    (g_both(X1, Y0) | g_both(Y0, X1)))))) &
86.84/87.43	            (~((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))))))))|
86.84/87.43	         (g_both(X1, '#sk1') &
86.84/87.43	          ((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))) |
86.84/87.43	           (!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0)))))))),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['21'])).
86.84/87.43	tff('23', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      ~ (g_false_only(X1, '#sk1') &
86.84/87.43	         ((!!((^[Y0 : $i]: (g_false_only(X1, Y0) | g_false_only(Y0, X1))))) |
86.84/87.43	          ((??((^[Y0 : $i]:
86.84/87.43	                  ((~(g_false_only(X1, Y0)))&(~(g_false_only(Y0, X1)))&
86.84/87.43	                   (g_both(X1, Y0) | g_both(Y0, X1)))))) &
86.84/87.43	           (~((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0)))))))))),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['22'])).
86.84/87.43	tff('24', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      (~ g_false_only(X1, '#sk1')
86.84/87.43	       | ~ ((!!((^[Y0 : $i]: (g_false_only(X1, Y0) | g_false_only(Y0, X1))))) |
86.84/87.43	            ((??((^[Y0 : $i]:
86.84/87.43	                    ((~(g_false_only(X1, Y0)))&(~(g_false_only(Y0, X1)))&
86.84/87.43	                     (g_both(X1, Y0) | g_both(Y0, X1)))))) &
86.84/87.43	             (~((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0)))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['23'])).
86.84/87.43	tff('25', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      (~ (!!((^[Y0 : $i]: (g_false_only(X1, Y0) | g_false_only(Y0, X1)))))
86.84/87.43	       | ~ g_false_only(X1, '#sk1')),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['24'])).
86.84/87.43	tff('26', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      (~ (g_false_only(X1, '#sk3'(X1)) | g_false_only('#sk3'(X1), X1))
86.84/87.43	       | ~ g_false_only(X1, '#sk1')),
86.84/87.43	    inference('lazy_cnf_exists', [status(thm)], ['25'])).
86.84/87.43	tff('27', plain,
86.84/87.43	    ![X1]: (~ g_false_only('#sk3'(X1), X1) | ~ g_false_only(X1, '#sk1')),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['26'])).
86.84/87.43	tff('28', plain,
86.84/87.43	    (( g_true_only('#sk3'('#sk2'), '#sk2') | ~ g_false_only('#sk2', '#sk1')))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['19', '27'])).
86.84/87.43	tff('29', plain,
86.84/87.43	    (~ g_false_only('#sk2', '#sk1')) <= (~ ( g_false_only('#sk2', '#sk1'))),
86.84/87.43	    inference('split', [status(esa)], ['28'])).
86.84/87.43	tff('30', plain,
86.84/87.43	    (( g_both('#sk2', '#sk1') |  g_true_only('#sk2', '#sk1')))
86.84/87.43	      <= (~ ( g_false_only('#sk2', '#sk1'))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['17', '29'])).
86.84/87.43	tff('31', plain, ( g_both('#sk2', '#sk1')) <= (( g_both('#sk2', '#sk1'))),
86.84/87.43	    inference('split', [status(esa)], ['30'])).
86.84/87.43	tff('32', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      (~ ((??((^[Y0 : $i]:
86.84/87.43	                 ((~(g_false_only(X1, Y0)))&(~(g_false_only(Y0, X1)))&
86.84/87.43	                  (g_both(X1, Y0) | g_both(Y0, X1)))))) &
86.84/87.43	          (~((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))))))
86.84/87.43	       | ~ g_false_only(X1, '#sk1')),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['24'])).
86.84/87.43	tff('33', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      (~ (??((^[Y0 : $i]:
86.84/87.43	                ((~(g_false_only(X1, Y0)))&(~(g_false_only(Y0, X1)))&
86.84/87.43	                 (g_both(X1, Y0) | g_both(Y0, X1))))))
86.84/87.43	       |  (??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0)))))
86.84/87.43	       | ~ g_false_only(X1, '#sk1')),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['32'])).
86.84/87.43	tff('34', plain,
86.84/87.43	    ![X1, X2]:
86.84/87.43	      (~ ((~(g_false_only(X1, X2)))&(~(g_false_only(X2, X1)))&
86.84/87.43	          (g_both(X1, X2) | g_both(X2, X1)))
86.84/87.43	       | ~ g_false_only(X1, '#sk1')
86.84/87.43	       |  (??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0)))))),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['33'])).
86.84/87.43	tff('35', plain,
86.84/87.43	    ![X1, X2]:
86.84/87.43	      ( g_false_only(X1, X2)
86.84/87.43	       |  g_false_only(X2, X1)
86.84/87.43	       | ~ (g_both(X1, X2) | g_both(X2, X1))
86.84/87.43	       |  (??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0)))))
86.84/87.43	       | ~ g_false_only(X1, '#sk1')),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['34'])).
86.84/87.43	tff('36', plain,
86.84/87.43	    ![X1, X2]:
86.84/87.43	      (~ g_both(X2, X1)
86.84/87.43	       | ~ g_false_only(X1, '#sk1')
86.84/87.43	       |  (??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0)))))
86.84/87.43	       |  g_false_only(X2, X1)
86.84/87.43	       |  g_false_only(X1, X2)),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['35'])).
86.84/87.43	tff('37', plain,
86.84/87.43	    ![X1, X2]:
86.84/87.43	      ( (g_true_only('#sk4'(X1), X1) & g_true_only(X1, '#sk4'(X1)))
86.84/87.43	       |  g_false_only(X1, X2)
86.84/87.43	       |  g_false_only(X2, X1)
86.84/87.43	       | ~ g_false_only(X1, '#sk1')
86.84/87.43	       | ~ g_both(X2, X1)),
86.84/87.43	    inference('lazy_cnf_exists', [status(thm)], ['36'])).
86.84/87.43	tff('38', plain,
86.84/87.43	    ![X1, X2]:
86.84/87.43	      ( g_true_only('#sk4'(X1), X1)
86.84/87.43	       | ~ g_both(X2, X1)
86.84/87.43	       | ~ g_false_only(X1, '#sk1')
86.84/87.43	       |  g_false_only(X2, X1)
86.84/87.43	       |  g_false_only(X1, X2)),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['37'])).
86.84/87.43	tff('39', plain,
86.84/87.43	    (( g_true_only('#sk4'('#sk1'), '#sk1')
86.84/87.43	      | ~ g_false_only('#sk1', '#sk1')
86.84/87.43	      |  g_false_only('#sk2', '#sk1')
86.84/87.43	      |  g_false_only('#sk1', '#sk2'))) <= (( g_both('#sk2', '#sk1'))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['31', '38'])).
86.84/87.43	tff('40', plain,
86.84/87.43	    (~ g_false_only('#sk1', '#sk1')) <= (~ ( g_false_only('#sk1', '#sk1'))),
86.84/87.43	    inference('split', [status(esa)], ['39'])).
86.84/87.43	tff('41', plain,
86.84/87.43	    (( g_both('#sk1', '#sk1') |  g_true_only('#sk1', '#sk1')))
86.84/87.43	      <= (~ ( g_false_only('#sk1', '#sk1'))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['16', '40'])).
86.84/87.43	tff('42', plain, ( g_both('#sk1', '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.43	    inference('split', [status(esa)], ['41'])).
86.84/87.43	tff('43', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      ~ (g_both(X1, '#sk1') &
86.84/87.43	         ((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))) |
86.84/87.43	          (!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0))))))),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['22'])).
86.84/87.43	tff('44', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      (~ g_both(X1, '#sk1')
86.84/87.43	       | ~ ((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))) |
86.84/87.43	            (!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['43'])).
86.84/87.43	tff('45', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      (~ (!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0)))))
86.84/87.43	       | ~ g_both(X1, '#sk1')),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['44'])).
86.84/87.43	tff('46', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      (~ (g_false_only('#sk3'(X1), X1) | g_false_only(X1, '#sk3'(X1)))
86.84/87.43	       | ~ g_both(X1, '#sk1')),
86.84/87.43	    inference('lazy_cnf_exists', [status(thm)], ['45'])).
86.84/87.43	tff('47', plain,
86.84/87.43	    ![X1]: (~ g_false_only('#sk3'(X1), X1) | ~ g_both(X1, '#sk1')),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['46'])).
86.84/87.43	tff('48', plain,
86.84/87.43	    (~ g_false_only('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['42', '47'])).
86.84/87.43	tff('49', plain,
86.84/87.43	    (( g_true_only('#sk1', '#sk4'('#sk1'))
86.84/87.43	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0)))))))))) & 
86.84/87.43	          ( g_both('#sk1', '#sk1'))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['12', '48'])).
86.84/87.43	tff('50', plain,
86.84/87.43	    ~
86.84/87.43	    ( (??((^[Y0 : $i]:
86.84/87.43	             (!!((^[Y1 : $i]:
86.84/87.43	                    ((g_false_only(Y1, Y0) &
86.84/87.43	                      (??((^[Y2 : $i]:
86.84/87.43	                             (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                     ((!!((^[Y2 : $i]:
86.84/87.43	                             (g_false_only(Y2, Y1) | g_false_only(Y1, Y2))))) &
86.84/87.43	                      g_true_only(Y1, Y0)))))))))) | 
86.84/87.43	    ( g_true_only('#sk1', '#sk4'('#sk1'))) | ~ ( g_both('#sk1', '#sk1')) | 
86.84/87.43	    ( g_false_only('#sk1', '#sk3'('#sk1'))),
86.84/87.43	    inference('split', [status(esa)], ['49'])).
86.84/87.43	tff('51', plain,
86.84/87.43	    (![X1]:
86.84/87.43	       ( g_true_only('#sk4'(X1), X1)
86.84/87.43	        |  ((!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0))))) &
86.84/87.43	            g_true_only(X1, '#sk2'))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['8'])).
86.84/87.43	tff('52', plain,
86.84/87.43	    (![X1]:
86.84/87.43	       ( (!!((^[Y0 : $i]: (g_false_only(Y0, X1) | g_false_only(X1, Y0)))))
86.84/87.43	        |  g_true_only('#sk4'(X1), X1)))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['51'])).
86.84/87.43	tff('53', plain,
86.84/87.43	    (![X1, X2]:
86.84/87.43	       ( (g_false_only(X2, X1) | g_false_only(X1, X2))
86.84/87.43	        |  g_true_only('#sk4'(X1), X1)))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['52'])).
86.84/87.43	tff('54', plain,
86.84/87.43	    (![X1, X2]:
86.84/87.43	       ( g_false_only(X2, X1)
86.84/87.43	        |  g_false_only(X1, X2)
86.84/87.43	        |  g_true_only('#sk4'(X1), X1)))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0))))))))))),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['53'])).
86.84/87.43	tff('55', plain,
86.84/87.43	    (~ g_false_only('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['42', '47'])).
86.84/87.43	tff('56', plain,
86.84/87.43	    (( g_true_only('#sk4'('#sk1'), '#sk1')
86.84/87.43	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.43	      <= (( (??((^[Y0 : $i]:
86.84/87.43	                   (!!((^[Y1 : $i]:
86.84/87.43	                          ((g_false_only(Y1, Y0) &
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                           ((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2))))) &
86.84/87.43	                            g_true_only(Y1, Y0)))))))))) & 
86.84/87.43	          ( g_both('#sk1', '#sk1'))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['54', '55'])).
86.84/87.43	tff('57', plain,
86.84/87.43	    ( g_true_only('#sk4'('#sk1'), '#sk1')) | 
86.84/87.43	    ~
86.84/87.43	    ( (??((^[Y0 : $i]:
86.84/87.43	             (!!((^[Y1 : $i]:
86.84/87.43	                    ((g_false_only(Y1, Y0) &
86.84/87.43	                      (??((^[Y2 : $i]:
86.84/87.43	                             (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                     ((!!((^[Y2 : $i]:
86.84/87.43	                             (g_false_only(Y2, Y1) | g_false_only(Y1, Y2))))) &
86.84/87.43	                      g_true_only(Y1, Y0)))))))))) | 
86.84/87.43	    ~ ( g_both('#sk1', '#sk1')) | ( g_false_only('#sk1', '#sk3'('#sk1'))),
86.84/87.43	    inference('split', [status(esa)], ['56'])).
86.84/87.43	tff('58', plain,
86.84/87.43	    ~
86.84/87.43	    ( (??((^[Y0 : $i]:
86.84/87.43	             ((??((^[Y1 : $i]:
86.84/87.43	                     ((~((??((^[Y2 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))))&
86.84/87.43	                      (??((^[Y2 : $i]:
86.84/87.43	                             ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                              (~(g_false_only(Y2, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                      g_both(Y1, Y0))))) &
86.84/87.43	              (~((??((^[Y1 : $i]:
86.84/87.43	                        ((((!!((^[Y2 : $i]:
86.84/87.43	                                  (g_false_only(Y1, Y2) |
86.84/87.43	                                   g_false_only(Y2, Y1))))) |
86.84/87.43	                           (??((^[Y2 : $i]:
86.84/87.43	                                  (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) &
86.84/87.43	                          g_both(Y1, Y0))|
86.84/87.43	                         (g_false_only(Y1, Y0) &
86.84/87.43	                          (((??((^[Y2 : $i]:
86.84/87.43	                                   ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                            (~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y2, Y1) &
86.84/87.43	                                       g_true_only(Y1, Y2)))))))) |
86.84/87.43	                           (!!((^[Y2 : $i]:
86.84/87.43	                                  (g_false_only(Y2, Y1) |
86.84/87.43	                                   g_false_only(Y1, Y2)))))))|
86.84/87.43	                         ((((??((^[Y2 : $i]:
86.84/87.43	                                   ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                            (~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y2, Y1) &
86.84/87.43	                                       g_true_only(Y1, Y2)))))))) |
86.84/87.43	                           (??((^[Y2 : $i]:
86.84/87.43	                                  (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) &
86.84/87.43	                          g_true_only(Y1, Y0))))))))))))) | 
86.84/87.43	    ( (??((^[Y0 : $i]:
86.84/87.43	             (!!((^[Y1 : $i]:
86.84/87.43	                    ((g_false_only(Y1, Y0) &
86.84/87.43	                      (??((^[Y2 : $i]:
86.84/87.43	                             (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.43	                     ((!!((^[Y2 : $i]:
86.84/87.43	                             (g_false_only(Y2, Y1) | g_false_only(Y1, Y2))))) &
86.84/87.43	                      g_true_only(Y1, Y0)))))))))),
86.84/87.43	    inference('split', [status(esa)], ['2'])).
86.84/87.43	tff('59', plain,
86.84/87.43	    ![X1, X2]:
86.84/87.43	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.43	tff('60', plain,
86.84/87.43	    (~ g_false_only('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['42', '47'])).
86.84/87.43	tff('61', plain,
86.84/87.43	    (( g_both('#sk3'('#sk1'), '#sk1') |  g_true_only('#sk3'('#sk1'), '#sk1')))
86.84/87.43	      <= (( g_both('#sk1', '#sk1'))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['59', '60'])).
86.84/87.43	tff('62', plain,
86.84/87.43	    ( g_both('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.43	    inference('split', [status(esa)], ['61'])).
86.84/87.43	tff('63', plain,
86.84/87.43	    ( g_both('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.43	    inference('split', [status(esa)], ['61'])).
86.84/87.43	tff('64', plain,
86.84/87.43	    (~ (??((^[Y0 : $i]:
86.84/87.43	              ((??((^[Y1 : $i]:
86.84/87.43	                      ((~((??((^[Y2 : $i]:
86.84/87.43	                                 (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))))&
86.84/87.43	                       (??((^[Y2 : $i]:
86.84/87.43	                              ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                               (~(g_false_only(Y2, Y1)))&
86.84/87.43	                               (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                       g_both(Y1, Y0))))) &
86.84/87.43	               (~((??((^[Y1 : $i]:
86.84/87.43	                         ((((!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y1, Y2) |
86.84/87.43	                                    g_false_only(Y2, Y1))))) |
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) &
86.84/87.43	                           g_both(Y1, Y0))|
86.84/87.43	                          (g_false_only(Y1, Y0) &
86.84/87.43	                           (((??((^[Y2 : $i]:
86.84/87.43	                                    ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                     (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                     (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                             (~((??((^[Y2 : $i]:
86.84/87.43	                                       (g_true_only(Y2, Y1) &
86.84/87.43	                                        g_true_only(Y1, Y2)))))))) |
86.84/87.43	                            (!!((^[Y2 : $i]:
86.84/87.43	                                   (g_false_only(Y2, Y1) |
86.84/87.43	                                    g_false_only(Y1, Y2)))))))|
86.84/87.43	                          ((((??((^[Y2 : $i]:
86.84/87.43	                                    ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                     (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                     (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                             (~((??((^[Y2 : $i]:
86.84/87.43	                                       (g_true_only(Y2, Y1) &
86.84/87.43	                                        g_true_only(Y1, Y2)))))))) |
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) &
86.84/87.43	                           g_true_only(Y1, Y0)))))))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('split', [status(esa)], ['2'])).
86.84/87.43	tff('65', plain,
86.84/87.43	    (![X1]:
86.84/87.43	       ~ ((??((^[Y0 : $i]:
86.84/87.43	                 ((~((??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))))&
86.84/87.43	                  (??((^[Y1 : $i]:
86.84/87.43	                         ((g_both(Y0, Y1) | g_both(Y1, Y0))&
86.84/87.43	                          (~(g_false_only(Y1, Y0)))&(~(g_false_only(Y0, Y1)))))))&
86.84/87.43	                  g_both(Y0, X1))))) &
86.84/87.43	          (~((??((^[Y0 : $i]:
86.84/87.43	                    ((((!!((^[Y1 : $i]:
86.84/87.43	                              (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                       (??((^[Y1 : $i]:
86.84/87.43	                              (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                      g_both(Y0, X1))|
86.84/87.43	                     (g_false_only(Y0, X1) &
86.84/87.43	                      (((??((^[Y1 : $i]:
86.84/87.43	                               ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                                (~(g_false_only(Y1, Y0)))&
86.84/87.43	                                (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                        (~((??((^[Y1 : $i]:
86.84/87.43	                                  (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                       (!!((^[Y1 : $i]:
86.84/87.43	                              (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                     ((((??((^[Y1 : $i]:
86.84/87.43	                               ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                                (~(g_false_only(Y1, Y0)))&
86.84/87.43	                                (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                        (~((??((^[Y1 : $i]:
86.84/87.43	                                  (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                       (??((^[Y1 : $i]:
86.84/87.43	                              (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                      g_true_only(Y0, X1))))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['64'])).
86.84/87.43	tff('66', plain,
86.84/87.43	    (![X1]:
86.84/87.43	       (~ (??((^[Y0 : $i]:
86.84/87.43	                 ((~((??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))))&
86.84/87.43	                  (??((^[Y1 : $i]:
86.84/87.43	                         ((g_both(Y0, Y1) | g_both(Y1, Y0))&
86.84/87.43	                          (~(g_false_only(Y1, Y0)))&(~(g_false_only(Y0, Y1)))))))&
86.84/87.43	                  g_both(Y0, X1)))))
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['65'])).
86.84/87.43	tff('67', plain,
86.84/87.43	    (![X1, X2]:
86.84/87.43	       (~ ((~((??((^[Y0 : $i]: (g_true_only(X2, Y0) & g_true_only(Y0, X2)))))))&
86.84/87.43	           (??((^[Y0 : $i]:
86.84/87.43	                  ((g_both(X2, Y0) | g_both(Y0, X2))&
86.84/87.43	                   (~(g_false_only(Y0, X2)))&(~(g_false_only(X2, Y0)))))))&
86.84/87.43	           g_both(X2, X1))
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['66'])).
86.84/87.43	tff('68', plain,
86.84/87.43	    (![X1, X2]:
86.84/87.43	       ( (??((^[Y0 : $i]: (g_true_only(X2, Y0) & g_true_only(Y0, X2)))))
86.84/87.43	        | ~ (??((^[Y0 : $i]:
86.84/87.43	                   ((g_both(X2, Y0) | g_both(Y0, X2))&
86.84/87.43	                    (~(g_false_only(Y0, X2)))&(~(g_false_only(X2, Y0)))))))
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['67'])).
86.84/87.43	tff('69', plain,
86.84/87.43	    (![X1, X2]:
86.84/87.43	       ( (g_true_only(X2, '#sk4'(X2)) & g_true_only('#sk4'(X2), X2))
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        | ~ (??((^[Y0 : $i]:
86.84/87.43	                   ((g_both(X2, Y0) | g_both(Y0, X2))&
86.84/87.43	                    (~(g_false_only(Y0, X2)))&(~(g_false_only(X2, Y0)))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_exists', [status(thm)], ['68'])).
86.84/87.43	tff('70', plain,
86.84/87.43	    (![X1, X2]:
86.84/87.43	       ( g_true_only('#sk4'(X2), X2)
86.84/87.43	        | ~ (??((^[Y0 : $i]:
86.84/87.43	                   ((g_both(X2, Y0) | g_both(Y0, X2))&
86.84/87.43	                    (~(g_false_only(Y0, X2)))&(~(g_false_only(X2, Y0)))))))
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['69'])).
86.84/87.43	tff('71', plain,
86.84/87.43	    (![X1, X2, X3]:
86.84/87.43	       (~ ((g_both(X2, X3) | g_both(X3, X2))&(~(g_false_only(X3, X2)))&
86.84/87.43	           (~(g_false_only(X2, X3))))
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  g_true_only('#sk4'(X2), X2)))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['70'])).
86.84/87.43	tff('72', plain,
86.84/87.43	    (![X1, X2, X3]:
86.84/87.43	       (~ (g_both(X2, X3) | g_both(X3, X2))
86.84/87.43	        |  g_false_only(X3, X2)
86.84/87.43	        |  g_false_only(X2, X3)
86.84/87.43	        |  g_true_only('#sk4'(X2), X2)
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['71'])).
86.84/87.43	tff('73', plain,
86.84/87.43	    (![X1, X2, X3]:
86.84/87.43	       (~ (g_both(X2, X3) | g_both(X3, X2))
86.84/87.43	        |  g_false_only(X3, X2)
86.84/87.43	        |  g_false_only(X2, X3)
86.84/87.43	        |  g_true_only('#sk4'(X2), X2)
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['71'])).
86.84/87.43	tff('74', plain,
86.84/87.43	    ![X1]:
86.84/87.43	      (~ '#form5'(X1)
86.84/87.43	       |  (??((^[Y0 : $i]:
86.84/87.43	                 ((((!!((^[Y1 : $i]:
86.84/87.43	                           (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                    (??((^[Y1 : $i]:
86.84/87.43	                           (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                   g_both(Y0, X1))|
86.84/87.43	                  (g_false_only(Y0, X1) &
86.84/87.43	                   (((??((^[Y1 : $i]:
86.84/87.43	                            ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                             (~(g_false_only(Y1, Y0)))&
86.84/87.43	                             (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                     (~((??((^[Y1 : $i]:
86.84/87.43	                               (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                    (!!((^[Y1 : $i]:
86.84/87.43	                           (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                  ((((??((^[Y1 : $i]:
86.84/87.43	                            ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                             (~(g_false_only(Y1, Y0)))&
86.84/87.43	                             (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                     (~((??((^[Y1 : $i]:
86.84/87.43	                               (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                    (??((^[Y1 : $i]:
86.84/87.43	                           (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                   g_true_only(Y0, X1))))))),
86.84/87.43	    define([status(thm)])).
86.84/87.43	tff('75', plain,
86.84/87.43	    (![X1, X2, X3]:
86.84/87.43	       ( '#form5'(X1)
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  g_true_only('#sk4'(X2), X2)
86.84/87.43	        |  g_false_only(X2, X3)
86.84/87.43	        |  g_false_only(X3, X2)
86.84/87.43	        | ~ (g_both(X2, X3) | g_both(X3, X2))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('renaming', [status(thm)], ['72', '74'])).
86.84/87.43	tff('76', plain,
86.84/87.43	    (![X1, X2, X3]:
86.84/87.43	       (~ g_both(X2, X3)
86.84/87.43	        |  g_false_only(X3, X2)
86.84/87.43	        |  g_false_only(X2, X3)
86.84/87.43	        |  g_true_only('#sk4'(X2), X2)
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  '#form5'(X1)))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_or', [status(thm)], ['75'])).
86.84/87.43	tff('77', plain,
86.84/87.43	    (![X0]:
86.84/87.43	       ( g_false_only('#sk1', '#sk3'('#sk1'))
86.84/87.43	        |  g_false_only('#sk3'('#sk1'), '#sk1')
86.84/87.43	        |  g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1'))
86.84/87.43	        | ~ g_both('#sk3'('#sk1'), X0)
86.84/87.43	        |  '#form5'(X0)))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0))))))))))))) & 
86.84/87.43	          ( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['63', '76'])).
86.84/87.43	tff('78', plain,
86.84/87.43	    (![X0]: ( '#form5'(X0) | ~ g_both('#sk3'('#sk1'), X0)))
86.84/87.43	      <= ((![X0]: ( '#form5'(X0) | ~ g_both('#sk3'('#sk1'), X0)))),
86.84/87.43	    inference('split', [status(esa)], ['77'])).
86.84/87.43	tff('79', plain,
86.84/87.43	    ( '#form5'('#sk1'))
86.84/87.43	      <= (( g_both('#sk3'('#sk1'), '#sk1')) & 
86.84/87.43	          (![X0]: ( '#form5'(X0) | ~ g_both('#sk3'('#sk1'), X0)))),
86.84/87.43	    inference('s_sup-', [status(thm)], ['62', '78'])).
86.84/87.43	tff('80', plain, ( g_both('#sk1', '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.43	    inference('split', [status(esa)], ['41'])).
86.84/87.43	tff('81', plain,
86.84/87.43	    (![X1, X2]:
86.84/87.43	       ( g_true_only(X2, '#sk4'(X2))
86.84/87.43	        | ~ (??((^[Y0 : $i]:
86.84/87.43	                   ((g_both(X2, Y0) | g_both(Y0, X2))&
86.84/87.43	                    (~(g_false_only(Y0, X2)))&(~(g_false_only(X2, Y0)))))))
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['69'])).
86.84/87.43	tff('82', plain,
86.84/87.43	    (![X1, X2, X3]:
86.84/87.43	       (~ ((g_both(X2, X3) | g_both(X3, X2))&(~(g_false_only(X3, X2)))&
86.84/87.43	           (~(g_false_only(X2, X3))))
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  g_true_only(X2, '#sk4'(X2))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_forall', [status(thm)], ['81'])).
86.84/87.43	tff('83', plain,
86.84/87.43	    (![X1, X2, X3]:
86.84/87.43	       (~ (g_both(X2, X3) | g_both(X3, X2))
86.84/87.43	        |  g_false_only(X3, X2)
86.84/87.43	        |  g_false_only(X2, X3)
86.84/87.43	        |  g_true_only(X2, '#sk4'(X2))
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y2, Y1) |
86.84/87.43	                                         g_false_only(Y1, Y2)))))))|
86.84/87.43	                               ((((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.43	                                  (~((??((^[Y2 : $i]:
86.84/87.43	                                            (g_true_only(Y2, Y1) &
86.84/87.43	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.43	    inference('lazy_cnf_and', [status(thm)], ['82'])).
86.84/87.43	tff('84', plain,
86.84/87.43	    (![X1, X2, X3]:
86.84/87.43	       (~ g_both(X2, X3)
86.84/87.43	        |  (??((^[Y0 : $i]:
86.84/87.43	                  ((((!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_both(Y0, X1))|
86.84/87.43	                   (g_false_only(Y0, X1) &
86.84/87.43	                    (((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (!!((^[Y1 : $i]:
86.84/87.43	                            (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.43	                   ((((??((^[Y1 : $i]:
86.84/87.43	                             ((~(g_false_only(Y0, Y1)))&
86.84/87.43	                              (~(g_false_only(Y1, Y0)))&
86.84/87.43	                              (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.43	                      (~((??((^[Y1 : $i]:
86.84/87.43	                                (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.43	                     (??((^[Y1 : $i]:
86.84/87.43	                            (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.43	                    g_true_only(Y0, X1))))))
86.84/87.43	        | ~ g_both(X2, X1)
86.84/87.43	        |  g_true_only(X2, '#sk4'(X2))
86.84/87.43	        |  g_false_only(X2, X3)
86.84/87.43	        |  g_false_only(X3, X2)))
86.84/87.43	      <= (~
86.84/87.43	          ( (??((^[Y0 : $i]:
86.84/87.43	                   ((??((^[Y1 : $i]:
86.84/87.43	                           ((~((??((^[Y2 : $i]:
86.84/87.43	                                      (g_true_only(Y1, Y2) &
86.84/87.43	                                       g_true_only(Y2, Y1)))))))&
86.84/87.43	                            (??((^[Y2 : $i]:
86.84/87.43	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.43	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.43	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.43	                            g_both(Y1, Y0))))) &
86.84/87.43	                    (~((??((^[Y1 : $i]:
86.84/87.43	                              ((((!!((^[Y2 : $i]:
86.84/87.43	                                        (g_false_only(Y1, Y2) |
86.84/87.43	                                         g_false_only(Y2, Y1))))) |
86.84/87.43	                                 (??((^[Y2 : $i]:
86.84/87.43	                                        (g_true_only(Y1, Y2) &
86.84/87.43	                                         g_true_only(Y2, Y1)))))) &
86.84/87.43	                                g_both(Y1, Y0))|
86.84/87.43	                               (g_false_only(Y1, Y0) &
86.84/87.43	                                (((??((^[Y2 : $i]:
86.84/87.43	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.43	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.44	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.44	                                  (~((??((^[Y2 : $i]:
86.84/87.44	                                            (g_true_only(Y2, Y1) &
86.84/87.44	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.44	                                 (!!((^[Y2 : $i]:
86.84/87.44	                                        (g_false_only(Y2, Y1) |
86.84/87.44	                                         g_false_only(Y1, Y2)))))))|
86.84/87.44	                               ((((??((^[Y2 : $i]:
86.84/87.44	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.44	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.44	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.44	                                  (~((??((^[Y2 : $i]:
86.84/87.44	                                            (g_true_only(Y2, Y1) &
86.84/87.44	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.44	                                 (??((^[Y2 : $i]:
86.84/87.44	                                        (g_true_only(Y1, Y2) &
86.84/87.44	                                         g_true_only(Y2, Y1)))))) &
86.84/87.44	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['83'])).
86.84/87.44	tff('85', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form5'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 ((((!!((^[Y1 : $i]:
86.84/87.44	                           (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.44	                    (??((^[Y1 : $i]:
86.84/87.44	                           (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.44	                   g_both(Y0, X1))|
86.84/87.44	                  (g_false_only(Y0, X1) &
86.84/87.44	                   (((??((^[Y1 : $i]:
86.84/87.44	                            ((~(g_false_only(Y0, Y1)))&
86.84/87.44	                             (~(g_false_only(Y1, Y0)))&
86.84/87.44	                             (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.44	                     (~((??((^[Y1 : $i]:
86.84/87.44	                               (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.44	                    (!!((^[Y1 : $i]:
86.84/87.44	                           (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.44	                  ((((??((^[Y1 : $i]:
86.84/87.44	                            ((~(g_false_only(Y0, Y1)))&
86.84/87.44	                             (~(g_false_only(Y1, Y0)))&
86.84/87.44	                             (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.44	                     (~((??((^[Y1 : $i]:
86.84/87.44	                               (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.44	                    (??((^[Y1 : $i]:
86.84/87.44	                           (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.44	                   g_true_only(Y0, X1))))))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('86', plain,
86.84/87.44	    (![X1, X2, X3]:
86.84/87.44	       ( '#form5'(X1)
86.84/87.44	        |  g_false_only(X3, X2)
86.84/87.44	        |  g_false_only(X2, X3)
86.84/87.44	        |  g_true_only(X2, '#sk4'(X2))
86.84/87.44	        | ~ g_both(X2, X1)
86.84/87.44	        | ~ g_both(X2, X3)))
86.84/87.44	      <= (~
86.84/87.44	          ( (??((^[Y0 : $i]:
86.84/87.44	                   ((??((^[Y1 : $i]:
86.84/87.44	                           ((~((??((^[Y2 : $i]:
86.84/87.44	                                      (g_true_only(Y1, Y2) &
86.84/87.44	                                       g_true_only(Y2, Y1)))))))&
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.44	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.44	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.44	                            g_both(Y1, Y0))))) &
86.84/87.44	                    (~((??((^[Y1 : $i]:
86.84/87.44	                              ((((!!((^[Y2 : $i]:
86.84/87.44	                                        (g_false_only(Y1, Y2) |
86.84/87.44	                                         g_false_only(Y2, Y1))))) |
86.84/87.44	                                 (??((^[Y2 : $i]:
86.84/87.44	                                        (g_true_only(Y1, Y2) &
86.84/87.44	                                         g_true_only(Y2, Y1)))))) &
86.84/87.44	                                g_both(Y1, Y0))|
86.84/87.44	                               (g_false_only(Y1, Y0) &
86.84/87.44	                                (((??((^[Y2 : $i]:
86.84/87.44	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.44	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.44	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.44	                                  (~((??((^[Y2 : $i]:
86.84/87.44	                                            (g_true_only(Y2, Y1) &
86.84/87.44	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.44	                                 (!!((^[Y2 : $i]:
86.84/87.44	                                        (g_false_only(Y2, Y1) |
86.84/87.44	                                         g_false_only(Y1, Y2)))))))|
86.84/87.44	                               ((((??((^[Y2 : $i]:
86.84/87.44	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.44	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.44	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.44	                                  (~((??((^[Y2 : $i]:
86.84/87.44	                                            (g_true_only(Y2, Y1) &
86.84/87.44	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.44	                                 (??((^[Y2 : $i]:
86.84/87.44	                                        (g_true_only(Y1, Y2) &
86.84/87.44	                                         g_true_only(Y2, Y1)))))) &
86.84/87.44	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.44	    inference('renaming', [status(thm)], ['84', '85'])).
86.84/87.44	tff('87', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( '#form5'('#sk1')
86.84/87.44	        |  g_false_only(X0, '#sk1')
86.84/87.44	        |  g_false_only('#sk1', X0)
86.84/87.44	        |  g_true_only('#sk1', '#sk4'('#sk1'))
86.84/87.44	        | ~ g_both('#sk1', X0)))
86.84/87.44	      <= (~
86.84/87.44	          ( (??((^[Y0 : $i]:
86.84/87.44	                   ((??((^[Y1 : $i]:
86.84/87.44	                           ((~((??((^[Y2 : $i]:
86.84/87.44	                                      (g_true_only(Y1, Y2) &
86.84/87.44	                                       g_true_only(Y2, Y1)))))))&
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.44	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.44	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.44	                            g_both(Y1, Y0))))) &
86.84/87.44	                    (~((??((^[Y1 : $i]:
86.84/87.44	                              ((((!!((^[Y2 : $i]:
86.84/87.44	                                        (g_false_only(Y1, Y2) |
86.84/87.44	                                         g_false_only(Y2, Y1))))) |
86.84/87.44	                                 (??((^[Y2 : $i]:
86.84/87.44	                                        (g_true_only(Y1, Y2) &
86.84/87.44	                                         g_true_only(Y2, Y1)))))) &
86.84/87.44	                                g_both(Y1, Y0))|
86.84/87.44	                               (g_false_only(Y1, Y0) &
86.84/87.44	                                (((??((^[Y2 : $i]:
86.84/87.44	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.44	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.44	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.44	                                  (~((??((^[Y2 : $i]:
86.84/87.44	                                            (g_true_only(Y2, Y1) &
86.84/87.44	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.44	                                 (!!((^[Y2 : $i]:
86.84/87.44	                                        (g_false_only(Y2, Y1) |
86.84/87.44	                                         g_false_only(Y1, Y2)))))))|
86.84/87.44	                               ((((??((^[Y2 : $i]:
86.84/87.44	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.44	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.44	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.44	                                  (~((??((^[Y2 : $i]:
86.84/87.44	                                            (g_true_only(Y2, Y1) &
86.84/87.44	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.44	                                 (??((^[Y2 : $i]:
86.84/87.44	                                        (g_true_only(Y1, Y2) &
86.84/87.44	                                         g_true_only(Y2, Y1)))))) &
86.84/87.44	                                g_true_only(Y1, Y0))))))))))))) & 
86.84/87.44	          ( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['80', '86'])).
86.84/87.44	tff('88', plain, ( '#form5'('#sk1')) <= (( '#form5'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['87'])).
86.84/87.44	tff('89', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form5'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 ((((!!((^[Y1 : $i]:
86.84/87.44	                           (g_false_only(Y0, Y1) | g_false_only(Y1, Y0))))) |
86.84/87.44	                    (??((^[Y1 : $i]:
86.84/87.44	                           (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.44	                   g_both(Y0, X1))|
86.84/87.44	                  (g_false_only(Y0, X1) &
86.84/87.44	                   (((??((^[Y1 : $i]:
86.84/87.44	                            ((~(g_false_only(Y0, Y1)))&
86.84/87.44	                             (~(g_false_only(Y1, Y0)))&
86.84/87.44	                             (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.44	                     (~((??((^[Y1 : $i]:
86.84/87.44	                               (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.44	                    (!!((^[Y1 : $i]:
86.84/87.44	                           (g_false_only(Y1, Y0) | g_false_only(Y0, Y1)))))))|
86.84/87.44	                  ((((??((^[Y1 : $i]:
86.84/87.44	                            ((~(g_false_only(Y0, Y1)))&
86.84/87.44	                             (~(g_false_only(Y1, Y0)))&
86.84/87.44	                             (g_both(Y1, Y0) | g_both(Y0, Y1)))))) &
86.84/87.44	                     (~((??((^[Y1 : $i]:
86.84/87.44	                               (g_true_only(Y1, Y0) & g_true_only(Y0, Y1)))))))) |
86.84/87.44	                    (??((^[Y1 : $i]:
86.84/87.44	                           (g_true_only(Y0, Y1) & g_true_only(Y1, Y0)))))) &
86.84/87.44	                   g_true_only(Y0, X1))))))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('90', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( ((((!!((^[Y0 : $i]:
86.84/87.44	                  (g_false_only('#sk6'(X1), Y0) |
86.84/87.44	                   g_false_only(Y0, '#sk6'(X1)))))) |
86.84/87.44	           (??((^[Y0 : $i]:
86.84/87.44	                  (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	          g_both('#sk6'(X1), X1))|
86.84/87.44	         (g_false_only('#sk6'(X1), X1) &
86.84/87.44	          (((??((^[Y0 : $i]:
86.84/87.44	                   ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                    (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                    (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	            (~((??((^[Y0 : $i]:
86.84/87.44	                      (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                       g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	           (!!((^[Y0 : $i]:
86.84/87.44	                  (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                   g_false_only('#sk6'(X1), Y0)))))))|
86.84/87.44	         ((((??((^[Y0 : $i]:
86.84/87.44	                   ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                    (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                    (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	            (~((??((^[Y0 : $i]:
86.84/87.44	                      (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                       g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	           (??((^[Y0 : $i]:
86.84/87.44	                  (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	          g_true_only('#sk6'(X1), X1)))
86.84/87.44	       | ~ '#form5'(X1)),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['89'])).
86.84/87.44	tff('91', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (((!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only('#sk6'(X1), Y0) | g_false_only(Y0, '#sk6'(X1)))))) |
86.84/87.44	          (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	         g_both('#sk6'(X1), X1))
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))
86.84/87.44	       |  ((((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	           g_true_only('#sk6'(X1), X1))
86.84/87.44	       | ~ '#form5'(X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['90'])).
86.84/87.44	tff('92', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( ((!!((^[Y0 : $i]:
86.84/87.44	                (g_false_only('#sk6'(X1), Y0) | g_false_only(Y0, '#sk6'(X1)))))) |
86.84/87.44	         (??((^[Y0 : $i]:
86.84/87.44	                (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1)))))))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  ((((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	           g_true_only('#sk6'(X1), X1))
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['91'])).
86.84/87.44	tff('93', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (!!((^[Y0 : $i]:
86.84/87.44	               (g_false_only('#sk6'(X1), Y0) | g_false_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))
86.84/87.44	       |  ((((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	           g_true_only('#sk6'(X1), X1))
86.84/87.44	       | ~ '#form5'(X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['92'])).
86.84/87.44	tff('94', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( (g_false_only('#sk6'(X1), X2) | g_false_only(X2, '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  ((((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	           g_true_only('#sk6'(X1), X1))
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['93'])).
86.84/87.44	tff('95', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))
86.84/87.44	       |  ((((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	           g_true_only('#sk6'(X1), X1))
86.84/87.44	       | ~ '#form5'(X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['94'])).
86.84/87.44	tff('96', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	         g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  ((((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	           g_true_only('#sk6'(X1), X1))
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['95'])).
86.84/87.44	tff('97', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  ((((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	           g_true_only('#sk6'(X1), X1))
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['91'])).
86.84/87.44	tff('98', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (((??((^[Y0 : $i]:
86.84/87.44	                 ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                  (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                  (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	          (~((??((^[Y0 : $i]:
86.84/87.44	                    (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                     g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	         (??((^[Y0 : $i]:
86.84/87.44	                (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1)))))))
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['97'])).
86.84/87.44	tff('99', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( ((??((^[Y0 : $i]:
86.84/87.44	                ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                 (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                 (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	         (~((??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only(Y0, '#sk6'(X1)) & g_true_only('#sk6'(X1), Y0))))))))
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['98'])).
86.84/87.44	tff('100', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (??((^[Y0 : $i]:
86.84/87.44	               ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0))))))
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['99'])).
86.84/87.44	tff('101', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form7'(X1)
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('102', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  ((((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))) &
86.84/87.44	           g_true_only('#sk6'(X1), X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))),
86.84/87.44	    inference('renaming', [status(thm)], ['96', '101'])).
86.84/87.44	tff('103', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only('#sk6'(X1), X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['102'])).
86.84/87.44	tff('104', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1)))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['103'])).
86.84/87.44	tff('105', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	        |  '#form7'('#sk1')
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        |  g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  g_true_only('#sk6'('#sk1'), '#sk1')))
86.84/87.44	      <= (( '#form5'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['88', '104'])).
86.84/87.44	tff('106', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1'))))
86.84/87.44	      <= ((![X0]:
86.84/87.44	             ( g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	              |  g_false_only(X0, '#sk6'('#sk1'))))),
86.84/87.44	    inference('split', [status(esa)], ['105'])).
86.84/87.44	tff('107', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (??((^[Y0 : $i]:
86.84/87.44	               ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0))))))
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['99'])).
86.84/87.44	tff('108', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form7'(X1)
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('109', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( '#form7'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                  (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                  (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0))))))),
86.84/87.44	    inference('renaming', [status(thm)], ['107', '108'])).
86.84/87.44	tff('110', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	         g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                  (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                  (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0))))))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       |  '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['109'])).
86.84/87.44	tff('111', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1)))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                  (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                  (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['110'])).
86.84/87.44	tff('112', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( ((~(g_false_only('#sk6'(X1), '#sk8'(X1))))&
86.84/87.44	         (~(g_false_only('#sk8'(X1), '#sk6'(X1))))&
86.84/87.44	         (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1))))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1)))),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['111'])).
86.84/87.44	tff('113', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ g_false_only('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       |  g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1)))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['112'])).
86.84/87.44	tff('114', plain,
86.84/87.44	    (( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))
86.84/87.44	      |  g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	      |  '#form7'('#sk1')
86.84/87.44	      |  g_both('#sk6'('#sk1'), '#sk1')
86.84/87.44	      | ~ '#form5'('#sk1')))
86.84/87.44	      <= ((![X0]:
86.84/87.44	             ( g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	              |  g_false_only(X0, '#sk6'('#sk1'))))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['106', '113'])).
86.84/87.44	tff('115', plain, (~ '#form5'('#sk1')) <= (~ ( '#form5'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['114'])).
86.84/87.44	tff('116', plain,
86.84/87.44	    ($false)
86.84/87.44	      <= (~ ( '#form5'('#sk1')) & 
86.84/87.44	          ( g_both('#sk3'('#sk1'), '#sk1')) & 
86.84/87.44	          (![X0]: ( '#form5'(X0) | ~ g_both('#sk3'('#sk1'), X0)))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['79', '115'])).
86.84/87.44	tff('117', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.44	tff('118', plain, ( g_both('#sk1', '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['41'])).
86.84/87.44	tff('119', plain,
86.84/87.44	    ![X1]: (~ g_false_only(X1, '#sk3'(X1)) | ~ g_both(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['46'])).
86.84/87.44	tff('120', plain,
86.84/87.44	    (~ g_false_only('#sk1', '#sk3'('#sk1'))) <= (( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['118', '119'])).
86.84/87.44	tff('121', plain,
86.84/87.44	    (( g_both('#sk1', '#sk3'('#sk1')) |  g_true_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['117', '120'])).
86.84/87.44	tff('122', plain,
86.84/87.44	    ( g_both('#sk1', '#sk3'('#sk1'))) <= (( g_both('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['121'])).
86.84/87.44	tff('123', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ~ (g_true_only(X1, '#sk1') &
86.84/87.44	         ((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))) |
86.84/87.44	          ((~((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))))) &
86.84/87.44	           (??((^[Y0 : $i]:
86.84/87.44	                  ((~(g_false_only(Y0, X1)))&(~(g_false_only(X1, Y0)))&
86.84/87.44	                   (g_both(Y0, X1) | g_both(X1, Y0))))))))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['22'])).
86.84/87.44	tff('124', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ g_true_only(X1, '#sk1')
86.84/87.44	       | ~ ((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))) |
86.84/87.44	            ((~((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))))) &
86.84/87.44	             (??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only(Y0, X1)))&(~(g_false_only(X1, Y0)))&
86.84/87.44	                     (g_both(Y0, X1) | g_both(X1, Y0))))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['123'])).
86.84/87.44	tff('125', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ ((~((??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0))))))) &
86.84/87.44	          (??((^[Y0 : $i]:
86.84/87.44	                 ((~(g_false_only(Y0, X1)))&(~(g_false_only(X1, Y0)))&
86.84/87.44	                  (g_both(Y0, X1) | g_both(X1, Y0)))))))
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['124'])).
86.84/87.44	tff('126', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0)))))
86.84/87.44	       | ~ (??((^[Y0 : $i]:
86.84/87.44	                  ((~(g_false_only(Y0, X1)))&(~(g_false_only(X1, Y0)))&
86.84/87.44	                   (g_both(Y0, X1) | g_both(X1, Y0))))))
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['125'])).
86.84/87.44	tff('127', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (g_true_only('#sk4'(X1), X1) & g_true_only(X1, '#sk4'(X1)))
86.84/87.44	       | ~ g_true_only(X1, '#sk1')
86.84/87.44	       | ~ (??((^[Y0 : $i]:
86.84/87.44	                  ((~(g_false_only(Y0, X1)))&(~(g_false_only(X1, Y0)))&
86.84/87.44	                   (g_both(Y0, X1) | g_both(X1, Y0))))))),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['126'])).
86.84/87.44	tff('128', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( g_true_only(X1, '#sk4'(X1))
86.84/87.44	       | ~ (??((^[Y0 : $i]:
86.84/87.44	                  ((~(g_false_only(Y0, X1)))&(~(g_false_only(X1, Y0)))&
86.84/87.44	                   (g_both(Y0, X1) | g_both(X1, Y0))))))
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['127'])).
86.84/87.44	tff('129', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ ((~(g_false_only(X2, X1)))&(~(g_false_only(X1, X2)))&
86.84/87.44	          (g_both(X2, X1) | g_both(X1, X2)))
86.84/87.44	       | ~ g_true_only(X1, '#sk1')
86.84/87.44	       |  g_true_only(X1, '#sk4'(X1))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['128'])).
86.84/87.44	tff('130', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)
86.84/87.44	       | ~ (g_both(X2, X1) | g_both(X1, X2))
86.84/87.44	       |  g_true_only(X1, '#sk4'(X1))
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['129'])).
86.84/87.44	tff('131', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_both(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')
86.84/87.44	       |  g_true_only(X1, '#sk4'(X1))
86.84/87.44	       |  g_false_only(X1, X2)
86.84/87.44	       |  g_false_only(X2, X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['130'])).
86.84/87.44	tff('132', plain,
86.84/87.44	    ((~ g_true_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      |  g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))
86.84/87.44	      |  g_false_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['122', '131'])).
86.84/87.44	tff('133', plain,
86.84/87.44	    ( g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))) | 
86.84/87.44	    ~ ( g_true_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_both('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['132'])).
86.84/87.44	tff('134', plain,
86.84/87.44	    ( g_both('#sk1', '#sk3'('#sk1'))) <= (( g_both('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['121'])).
86.84/87.44	tff('135', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( g_true_only('#sk4'(X1), X1)
86.84/87.44	       | ~ (??((^[Y0 : $i]:
86.84/87.44	                  ((~(g_false_only(Y0, X1)))&(~(g_false_only(X1, Y0)))&
86.84/87.44	                   (g_both(Y0, X1) | g_both(X1, Y0))))))
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['127'])).
86.84/87.44	tff('136', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ ((~(g_false_only(X2, X1)))&(~(g_false_only(X1, X2)))&
86.84/87.44	          (g_both(X2, X1) | g_both(X1, X2)))
86.84/87.44	       | ~ g_true_only(X1, '#sk1')
86.84/87.44	       |  g_true_only('#sk4'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['135'])).
86.84/87.44	tff('137', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)
86.84/87.44	       | ~ (g_both(X2, X1) | g_both(X1, X2))
86.84/87.44	       |  g_true_only('#sk4'(X1), X1)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['136'])).
86.84/87.44	tff('138', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_both(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')
86.84/87.44	       |  g_true_only('#sk4'(X1), X1)
86.84/87.44	       |  g_false_only(X1, X2)
86.84/87.44	       |  g_false_only(X2, X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['137'])).
86.84/87.44	tff('139', plain,
86.84/87.44	    ((~ g_true_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      |  g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1'))
86.84/87.44	      |  g_false_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['134', '138'])).
86.84/87.44	tff('140', plain,
86.84/87.44	    ~ ( g_true_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_both('#sk1', '#sk3'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['139'])).
86.84/87.44	tff('141', plain,
86.84/87.44	    (![X1, X2]:
86.84/87.44	       ( g_false_only(X2, X1)
86.84/87.44	        |  g_false_only(X1, X2)
86.84/87.44	        |  g_true_only(X1, '#sk4'(X1))))
86.84/87.44	      <= (( (??((^[Y0 : $i]:
86.84/87.44	                   (!!((^[Y1 : $i]:
86.84/87.44	                          ((g_false_only(Y1, Y0) &
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.44	                           ((!!((^[Y2 : $i]:
86.84/87.44	                                   (g_false_only(Y2, Y1) |
86.84/87.44	                                    g_false_only(Y1, Y2))))) &
86.84/87.44	                            g_true_only(Y1, Y0))))))))))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['11'])).
86.84/87.44	tff('142', plain,
86.84/87.44	    (~ g_false_only('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['42', '47'])).
86.84/87.44	tff('143', plain,
86.84/87.44	    (( g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))
86.84/87.44	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( (??((^[Y0 : $i]:
86.84/87.44	                   (!!((^[Y1 : $i]:
86.84/87.44	                          ((g_false_only(Y1, Y0) &
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.44	                           ((!!((^[Y2 : $i]:
86.84/87.44	                                   (g_false_only(Y2, Y1) |
86.84/87.44	                                    g_false_only(Y1, Y2))))) &
86.84/87.44	                            g_true_only(Y1, Y0)))))))))) & 
86.84/87.44	          ( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['141', '142'])).
86.84/87.44	tff('144', plain,
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['143'])).
86.84/87.44	tff('145', plain,
86.84/87.44	    (~ g_false_only('#sk1', '#sk3'('#sk1'))) <= (( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['118', '119'])).
86.84/87.44	tff('146', plain,
86.84/87.44	    ~ ( g_false_only('#sk1', '#sk3'('#sk1'))) | ~ ( g_both('#sk1', '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['144', '145'])).
86.84/87.44	tff('147', plain,
86.84/87.44	    ( g_both('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['61'])).
86.84/87.44	tff('148', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_both(X1, X2)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')
86.84/87.44	       |  g_true_only('#sk4'(X1), X1)
86.84/87.44	       |  g_false_only(X1, X2)
86.84/87.44	       |  g_false_only(X2, X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['137'])).
86.84/87.44	tff('149', plain,
86.84/87.44	    ((~ g_true_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      |  g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1'))
86.84/87.44	      |  g_false_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['147', '148'])).
86.84/87.44	tff('150', plain,
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_false_only('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['149'])).
86.84/87.44	tff('151', plain,
86.84/87.44	    (~ g_false_only('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['42', '47'])).
86.84/87.44	tff('152', plain,
86.84/87.44	    ~ ( g_false_only('#sk3'('#sk1'), '#sk1')) | ~ ( g_both('#sk1', '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['150', '151'])).
86.84/87.44	tff('153', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.44	tff('154', plain,
86.84/87.44	    (~ g_false_only('#sk1', '#sk3'('#sk1'))) <= (( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['118', '119'])).
86.84/87.44	tff('155', plain,
86.84/87.44	    ( g_both('#sk1', '#sk3'('#sk1'))) <= (( g_both('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['121'])).
86.84/87.44	tff('156', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_both(X1, X2)
86.84/87.44	       | ~ g_false_only(X1, '#sk1')
86.84/87.44	       |  (??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0)))))
86.84/87.44	       |  g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['35'])).
86.84/87.44	tff('157', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( (g_true_only('#sk4'(X1), X1) & g_true_only(X1, '#sk4'(X1)))
86.84/87.44	       |  g_false_only(X1, X2)
86.84/87.44	       |  g_false_only(X2, X1)
86.84/87.44	       | ~ g_false_only(X1, '#sk1')
86.84/87.44	       | ~ g_both(X1, X2)),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['156'])).
86.84/87.44	tff('158', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, '#sk4'(X1))
86.84/87.44	       | ~ g_both(X1, X2)
86.84/87.44	       | ~ g_false_only(X1, '#sk1')
86.84/87.44	       |  g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['157'])).
86.84/87.44	tff('159', plain,
86.84/87.44	    (( g_true_only('#sk1', '#sk4'('#sk1'))
86.84/87.44	      | ~ g_false_only('#sk1', '#sk1')
86.84/87.44	      |  g_false_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['155', '158'])).
86.84/87.44	tff('160', plain,
86.84/87.44	    ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ~ ( g_both('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk1', '#sk4'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['159'])).
86.84/87.44	tff('161', plain,
86.84/87.44	    ( g_both('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['61'])).
86.84/87.44	tff('162', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, '#sk4'(X1))
86.84/87.44	       | ~ g_both(X2, X1)
86.84/87.44	       | ~ g_false_only(X1, '#sk1')
86.84/87.44	       |  g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['37'])).
86.84/87.44	tff('163', plain,
86.84/87.44	    (( g_true_only('#sk1', '#sk4'('#sk1'))
86.84/87.44	      | ~ g_false_only('#sk1', '#sk1')
86.84/87.44	      |  g_false_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['161', '162'])).
86.84/87.44	tff('164', plain,
86.84/87.44	    ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ~ ( g_both('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk1', '#sk4'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['163'])).
86.84/87.44	tff('165', plain,
86.84/87.44	    (![X1, X2]:
86.84/87.44	       ( g_false_only(X2, X1)
86.84/87.44	        |  g_false_only(X1, X2)
86.84/87.44	        |  g_true_only('#sk4'(X1), X1)))
86.84/87.44	      <= (( (??((^[Y0 : $i]:
86.84/87.44	                   (!!((^[Y1 : $i]:
86.84/87.44	                          ((g_false_only(Y1, Y0) &
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.44	                           ((!!((^[Y2 : $i]:
86.84/87.44	                                   (g_false_only(Y2, Y1) |
86.84/87.44	                                    g_false_only(Y1, Y2))))) &
86.84/87.44	                            g_true_only(Y1, Y0))))))))))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['53'])).
86.84/87.44	tff('166', plain,
86.84/87.44	    (~ g_false_only('#sk2', '#sk1')) <= (~ ( g_false_only('#sk2', '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['28'])).
86.84/87.44	tff('167', plain,
86.84/87.44	    (( g_true_only('#sk4'('#sk1'), '#sk1') |  g_false_only('#sk1', '#sk2')))
86.84/87.44	      <= (~ ( g_false_only('#sk2', '#sk1')) & 
86.84/87.44	          ( (??((^[Y0 : $i]:
86.84/87.44	                   (!!((^[Y1 : $i]:
86.84/87.44	                          ((g_false_only(Y1, Y0) &
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.44	                           ((!!((^[Y2 : $i]:
86.84/87.44	                                   (g_false_only(Y2, Y1) |
86.84/87.44	                                    g_false_only(Y1, Y2))))) &
86.84/87.44	                            g_true_only(Y1, Y0))))))))))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['165', '166'])).
86.84/87.44	tff('168', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['167'])).
86.84/87.44	tff('169', plain,
86.84/87.44	    (![X1, X2]:
86.84/87.44	       ( g_false_only(X2, X1)
86.84/87.44	        |  g_false_only(X1, X2)
86.84/87.44	        |  g_true_only(X1, '#sk4'(X1))))
86.84/87.44	      <= (( (??((^[Y0 : $i]:
86.84/87.44	                   (!!((^[Y1 : $i]:
86.84/87.44	                          ((g_false_only(Y1, Y0) &
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.44	                           ((!!((^[Y2 : $i]:
86.84/87.44	                                   (g_false_only(Y2, Y1) |
86.84/87.44	                                    g_false_only(Y1, Y2))))) &
86.84/87.44	                            g_true_only(Y1, Y0))))))))))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['11'])).
86.84/87.44	tff('170', plain,
86.84/87.44	    (~ g_false_only('#sk2', '#sk1')) <= (~ ( g_false_only('#sk2', '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['28'])).
86.84/87.44	tff('171', plain,
86.84/87.44	    (( g_true_only('#sk1', '#sk4'('#sk1')) |  g_false_only('#sk1', '#sk2')))
86.84/87.44	      <= (~ ( g_false_only('#sk2', '#sk1')) & 
86.84/87.44	          ( (??((^[Y0 : $i]:
86.84/87.44	                   (!!((^[Y1 : $i]:
86.84/87.44	                          ((g_false_only(Y1, Y0) &
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.44	                           ((!!((^[Y2 : $i]:
86.84/87.44	                                   (g_false_only(Y2, Y1) |
86.84/87.44	                                    g_false_only(Y1, Y2))))) &
86.84/87.44	                            g_true_only(Y1, Y0))))))))))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['169', '170'])).
86.84/87.44	tff('172', plain,
86.84/87.44	    ( g_true_only('#sk1', '#sk4'('#sk1')))
86.84/87.44	      <= (( g_true_only('#sk1', '#sk4'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['171'])).
86.84/87.44	tff('173', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ (??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0)))))
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['124'])).
86.84/87.44	tff('174', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ (g_true_only(X2, X1) & g_true_only(X1, X2))
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['173'])).
86.84/87.44	tff('175', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, X2)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['174'])).
86.84/87.44	tff('176', plain,
86.84/87.44	    ((~ g_true_only('#sk4'('#sk1'), '#sk1')
86.84/87.44	      | ~ g_true_only('#sk4'('#sk1'), '#sk1')))
86.84/87.44	      <= (( g_true_only('#sk1', '#sk4'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['172', '175'])).
86.84/87.44	tff('177', plain,
86.84/87.44	    (~ g_true_only('#sk4'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_true_only('#sk1', '#sk4'('#sk1')))),
86.84/87.44	    inference('simplify', [status(thm)], ['176'])).
86.84/87.44	tff('178', plain,
86.84/87.44	    ~ ( g_true_only('#sk1', '#sk4'('#sk1'))) | 
86.84/87.44	    ~ ( g_true_only('#sk4'('#sk1'), '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['168', '177'])).
86.84/87.44	tff('179', plain,
86.84/87.44	    (![X1, X2]:
86.84/87.44	       ( g_false_only(X2, X1)
86.84/87.44	        |  g_false_only(X1, X2)
86.84/87.44	        |  g_true_only(X1, '#sk4'(X1))))
86.84/87.44	      <= (( (??((^[Y0 : $i]:
86.84/87.44	                   (!!((^[Y1 : $i]:
86.84/87.44	                          ((g_false_only(Y1, Y0) &
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.44	                           ((!!((^[Y2 : $i]:
86.84/87.44	                                   (g_false_only(Y2, Y1) |
86.84/87.44	                                    g_false_only(Y1, Y2))))) &
86.84/87.44	                            g_true_only(Y1, Y0))))))))))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['11'])).
86.84/87.44	tff('180', plain,
86.84/87.44	    (~ g_false_only('#sk1', '#sk1')) <= (~ ( g_false_only('#sk1', '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['39'])).
86.84/87.44	tff('181', plain,
86.84/87.44	    (( g_true_only('#sk1', '#sk4'('#sk1')) |  g_false_only('#sk1', '#sk1')))
86.84/87.44	      <= (~ ( g_false_only('#sk1', '#sk1')) & 
86.84/87.44	          ( (??((^[Y0 : $i]:
86.84/87.44	                   (!!((^[Y1 : $i]:
86.84/87.44	                          ((g_false_only(Y1, Y0) &
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.44	                           ((!!((^[Y2 : $i]:
86.84/87.44	                                   (g_false_only(Y2, Y1) |
86.84/87.44	                                    g_false_only(Y1, Y2))))) &
86.84/87.44	                            g_true_only(Y1, Y0))))))))))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['179', '180'])).
86.84/87.44	tff('182', plain,
86.84/87.44	    ( g_false_only('#sk1', '#sk1')) <= (( g_false_only('#sk1', '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['181'])).
86.84/87.44	tff('183', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.44	tff('184', plain,
86.84/87.44	    ![X1]: (~ g_false_only('#sk3'(X1), X1) | ~ g_false_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['26'])).
86.84/87.44	tff('185', plain,
86.84/87.44	    ![X0]:
86.84/87.44	      ( g_both('#sk3'(X0), X0)
86.84/87.44	       |  g_true_only('#sk3'(X0), X0)
86.84/87.44	       | ~ g_false_only(X0, '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['183', '184'])).
86.84/87.44	tff('186', plain,
86.84/87.44	    (( g_both('#sk3'('#sk1'), '#sk1') |  g_true_only('#sk3'('#sk1'), '#sk1')))
86.84/87.44	      <= (( g_false_only('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['182', '185'])).
86.84/87.44	tff('187', plain,
86.84/87.44	    ( g_both('#sk3'('#sk1'), '#sk1')) | ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['186'])).
86.84/87.44	tff('188', plain,
86.84/87.44	    ( g_false_only('#sk1', '#sk1')) <= (( g_false_only('#sk1', '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['181'])).
86.84/87.44	tff('189', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.44	tff('190', plain,
86.84/87.44	    ![X1]: (~ g_false_only(X1, '#sk3'(X1)) | ~ g_false_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['26'])).
86.84/87.44	tff('191', plain,
86.84/87.44	    ![X0]:
86.84/87.44	      ( g_both(X0, '#sk3'(X0))
86.84/87.44	       |  g_true_only(X0, '#sk3'(X0))
86.84/87.44	       | ~ g_false_only(X0, '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['189', '190'])).
86.84/87.44	tff('192', plain,
86.84/87.44	    (( g_both('#sk1', '#sk3'('#sk1')) |  g_true_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( g_false_only('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['188', '191'])).
86.84/87.44	tff('193', plain,
86.84/87.44	    ( g_true_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_both('#sk1', '#sk3'('#sk1'))) | ~ ( g_false_only('#sk1', '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['192'])).
86.84/87.44	tff('194', plain,
86.84/87.44	    ( g_both('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['61'])).
86.84/87.44	tff('195', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only('#sk4'(X1), X1)
86.84/87.44	       | ~ g_both(X2, X1)
86.84/87.44	       | ~ g_false_only(X1, '#sk1')
86.84/87.44	       |  g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['37'])).
86.84/87.44	tff('196', plain,
86.84/87.44	    (( g_true_only('#sk4'('#sk1'), '#sk1')
86.84/87.44	      | ~ g_false_only('#sk1', '#sk1')
86.84/87.44	      |  g_false_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['194', '195'])).
86.84/87.44	tff('197', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_both('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['196'])).
86.84/87.44	tff('198', plain,
86.84/87.44	    ( g_both('#sk1', '#sk3'('#sk1'))) <= (( g_both('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['121'])).
86.84/87.44	tff('199', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only('#sk4'(X1), X1)
86.84/87.44	       | ~ g_both(X1, X2)
86.84/87.44	       | ~ g_false_only(X1, '#sk1')
86.84/87.44	       |  g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['157'])).
86.84/87.44	tff('200', plain,
86.84/87.44	    (( g_true_only('#sk4'('#sk1'), '#sk1')
86.84/87.44	      | ~ g_false_only('#sk1', '#sk1')
86.84/87.44	      |  g_false_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['198', '199'])).
86.84/87.44	tff('201', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_both('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['200'])).
86.84/87.44	tff('202', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.44	tff('203', plain,
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_false_only('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['149'])).
86.84/87.44	tff('204', plain,
86.84/87.44	    ![X1]: (~ g_false_only('#sk3'(X1), X1) | ~ g_false_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['26'])).
86.84/87.44	tff('205', plain,
86.84/87.44	    (~ g_false_only('#sk1', '#sk1'))
86.84/87.44	      <= (( g_false_only('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['203', '204'])).
86.84/87.44	tff('206', plain,
86.84/87.44	    (( g_both('#sk1', '#sk1') |  g_true_only('#sk1', '#sk1')))
86.84/87.44	      <= (( g_false_only('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['202', '205'])).
86.84/87.44	tff('207', plain,
86.84/87.44	    ( g_both('#sk1', '#sk1')) | ( g_true_only('#sk1', '#sk1')) | 
86.84/87.44	    ~ ( g_false_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['206'])).
86.84/87.44	tff('208', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.44	tff('209', plain,
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['143'])).
86.84/87.44	tff('210', plain,
86.84/87.44	    ![X1]: (~ g_false_only(X1, '#sk3'(X1)) | ~ g_false_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['26'])).
86.84/87.44	tff('211', plain,
86.84/87.44	    (~ g_false_only('#sk1', '#sk1'))
86.84/87.44	      <= (( g_false_only('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['209', '210'])).
86.84/87.44	tff('212', plain,
86.84/87.44	    (( g_both('#sk1', '#sk1') |  g_true_only('#sk1', '#sk1')))
86.84/87.44	      <= (( g_false_only('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['208', '211'])).
86.84/87.44	tff('213', plain,
86.84/87.44	    ( g_both('#sk1', '#sk1')) | ( g_true_only('#sk1', '#sk1')) | 
86.84/87.44	    ~ ( g_false_only('#sk1', '#sk3'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['212'])).
86.84/87.44	tff('214', plain,
86.84/87.44	    ( g_both('#sk1', '#sk1')) | ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk1', '#sk1')), inference('split', [status(esa)], ['41'])).
86.84/87.44	tff('215', plain,
86.84/87.44	    ( g_true_only('#sk1', '#sk1')) <= (( g_true_only('#sk1', '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['41'])).
86.84/87.44	tff('216', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, X2)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['174'])).
86.84/87.44	tff('217', plain, ~ ( g_true_only('#sk1', '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['215', '216'])).
86.84/87.44	tff('218', plain,
86.84/87.44	    ( g_true_only('#sk3'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_true_only('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['61'])).
86.84/87.44	tff('219', plain,
86.84/87.44	    ( g_true_only('#sk1', '#sk3'('#sk1')))
86.84/87.44	      <= (( g_true_only('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['121'])).
86.84/87.44	tff('220', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, X2)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['174'])).
86.84/87.44	tff('221', plain,
86.84/87.44	    ((~ g_true_only('#sk3'('#sk1'), '#sk1')
86.84/87.44	      | ~ g_true_only('#sk3'('#sk1'), '#sk1')))
86.84/87.44	      <= (( g_true_only('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['219', '220'])).
86.84/87.44	tff('222', plain,
86.84/87.44	    (~ g_true_only('#sk3'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_true_only('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('simplify', [status(thm)], ['221'])).
86.84/87.44	tff('223', plain,
86.84/87.44	    ~ ( g_true_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_true_only('#sk1', '#sk3'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['218', '222'])).
86.84/87.44	tff('224', plain, ( g_both('#sk1', '#sk1')),
86.84/87.44	    inference('sat_resolution*', [status(thm)],
86.84/87.44	              ['160', '164', '178', '187', '193', '197', '201', '207', 
86.84/87.44	               '213', '214', '217', '223'])).
86.84/87.44	tff('225', plain, ~ g_false_only('#sk1', '#sk3'('#sk1')),
86.84/87.44	    inference('simpl_trail', [status(thm)], ['154', '224'])).
86.84/87.44	tff('226', plain,
86.84/87.44	    ( g_both('#sk1', '#sk3'('#sk1')) |  g_true_only('#sk1', '#sk3'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['153', '225'])).
86.84/87.44	tff('227', plain,
86.84/87.44	    ( g_both('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk1', '#sk3'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['226'])).
86.84/87.44	tff('228', plain,
86.84/87.44	    ( g_true_only('#sk1', '#sk3'('#sk1')))
86.84/87.44	      <= (( g_true_only('#sk1', '#sk3'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['121'])).
86.84/87.44	tff('229', plain,
86.84/87.44	    ( g_true_only('#sk3'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_true_only('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['61'])).
86.84/87.44	tff('230', plain, ( g_both('#sk1', '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['41'])).
86.84/87.44	tff('231', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ (??((^[Y0 : $i]: (g_true_only(Y0, X1) & g_true_only(X1, Y0)))))
86.84/87.44	       | ~ g_both(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['44'])).
86.84/87.44	tff('232', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ (g_true_only(X2, X1) & g_true_only(X1, X2)) | ~ g_both(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['231'])).
86.84/87.44	tff('233', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, X1) | ~ g_true_only(X1, X2) | ~ g_both(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['232'])).
86.84/87.44	tff('234', plain,
86.84/87.44	    (![X0]: (~ g_true_only(X0, '#sk1') | ~ g_true_only('#sk1', X0)))
86.84/87.44	      <= (( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['230', '233'])).
86.84/87.44	tff('235', plain,
86.84/87.44	    (~ g_true_only('#sk1', '#sk3'('#sk1')))
86.84/87.44	      <= (( g_both('#sk1', '#sk1')) & ( g_true_only('#sk3'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['229', '234'])).
86.84/87.44	tff('236', plain,
86.84/87.44	    ~ ( g_true_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_true_only('#sk1', '#sk3'('#sk1'))) | ~ ( g_both('#sk1', '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['228', '235'])).
86.84/87.44	tff('237', plain,
86.84/87.44	    ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk1', '#sk4'('#sk1'))) | 
86.84/87.44	    ~ ( g_both('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['159'])).
86.84/87.44	tff('238', plain,
86.84/87.44	    ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk1', '#sk4'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_both('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['163'])).
86.84/87.44	tff('239', plain,
86.84/87.44	    ( g_both('#sk1', '#sk3'('#sk1'))) | ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk1', '#sk3'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['192'])).
86.84/87.44	tff('240', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ~ ( g_both('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['196'])).
86.84/87.44	tff('241', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.44	    ~ ( g_both('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['200'])).
86.84/87.44	tff('242', plain,
86.84/87.44	    (![X1, X2]:
86.84/87.44	       ( g_false_only(X2, X1)
86.84/87.44	        |  g_false_only(X1, X2)
86.84/87.44	        |  g_true_only('#sk4'(X1), X1)))
86.84/87.44	      <= (( (??((^[Y0 : $i]:
86.84/87.44	                   (!!((^[Y1 : $i]:
86.84/87.44	                          ((g_false_only(Y1, Y0) &
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.44	                           ((!!((^[Y2 : $i]:
86.84/87.44	                                   (g_false_only(Y2, Y1) |
86.84/87.44	                                    g_false_only(Y1, Y2))))) &
86.84/87.44	                            g_true_only(Y1, Y0))))))))))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['53'])).
86.84/87.44	tff('243', plain,
86.84/87.44	    (~ g_false_only('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['42', '47'])).
86.84/87.44	tff('244', plain,
86.84/87.44	    (( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1'))
86.84/87.44	      |  g_false_only('#sk1', '#sk3'('#sk1'))))
86.84/87.44	      <= (( (??((^[Y0 : $i]:
86.84/87.44	                   (!!((^[Y1 : $i]:
86.84/87.44	                          ((g_false_only(Y1, Y0) &
86.84/87.44	                            (??((^[Y2 : $i]:
86.84/87.44	                                   (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) |
86.84/87.44	                           ((!!((^[Y2 : $i]:
86.84/87.44	                                   (g_false_only(Y2, Y1) |
86.84/87.44	                                    g_false_only(Y1, Y2))))) &
86.84/87.44	                            g_true_only(Y1, Y0)))))))))) & 
86.84/87.44	          ( g_both('#sk1', '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['242', '243'])).
86.84/87.44	tff('245', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1')))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['244'])).
86.84/87.44	tff('246', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, X2)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['174'])).
86.84/87.44	tff('247', plain,
86.84/87.44	    ((~ g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))
86.84/87.44	      | ~ g_true_only('#sk3'('#sk1'), '#sk1')))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['245', '246'])).
86.84/87.44	tff('248', plain,
86.84/87.44	    ~ ( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1'))) | 
86.84/87.44	    ~ ( g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))) | 
86.84/87.44	    ~ ( g_true_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['247'])).
86.84/87.44	tff('249', plain,
86.84/87.44	    ( g_both('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk3'('#sk1'), '#sk1')) | ~ ( g_both('#sk1', '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['61'])).
86.84/87.44	tff('250', plain, ( g_both('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('sat_resolution*', [status(thm)],
86.84/87.44	              ['133', '140', '146', '152', '227', '236', '237', '238', 
86.84/87.44	               '178', '187', '239', '240', '241', '207', '213', '214', 
86.84/87.44	               '217', '223', '248', '249'])).
86.84/87.44	tff('251', plain,
86.84/87.44	    ~ (![X0]: ( '#form5'(X0) | ~ g_both('#sk3'('#sk1'), X0))) | 
86.84/87.44	    ( '#form5'('#sk1')),
86.84/87.44	    inference('simpl_trail', [status(thm)], ['116', '250'])).
86.84/87.44	tff('252', plain,
86.84/87.44	    ~ ( g_true_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))) | 
86.84/87.44	    ~ ( g_both('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk3'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['132'])).
86.84/87.44	tff('253', plain,
86.84/87.44	    ( g_true_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.44	    ( g_both('#sk1', '#sk3'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['226'])).
86.84/87.44	tff('254', plain,
86.84/87.44	    ~ ( g_true_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))) | 
86.84/87.44	    ~ ( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['247'])).
86.84/87.44	tff('255', plain, ( '#form5'('#sk1')) <= (( '#form5'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['87'])).
86.84/87.44	tff('256', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1)))
86.84/87.44	       |  g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1)))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['112'])).
86.84/87.44	tff('257', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( g_both('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       |  g_both('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1)))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['256'])).
86.84/87.44	tff('258', plain,
86.84/87.44	    (( g_both('#sk8'('#sk1'), '#sk6'('#sk1'))
86.84/87.44	      |  g_both('#sk6'('#sk1'), '#sk8'('#sk1'))
86.84/87.44	      |  g_both('#sk6'('#sk1'), '#sk1')
86.84/87.44	      |  '#form7'('#sk1')
86.84/87.44	      |  g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))))
86.84/87.44	      <= (( '#form5'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['255', '257'])).
86.84/87.44	tff('259', plain,
86.84/87.44	    ( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('260', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, '#sk4'(X1))
86.84/87.44	       | ~ g_both(X2, X1)
86.84/87.44	       | ~ g_false_only(X1, '#sk1')
86.84/87.44	       |  g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['37'])).
86.84/87.44	tff('261', plain,
86.84/87.44	    (( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	      | ~ g_false_only('#sk6'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))
86.84/87.44	      |  g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['259', '260'])).
86.84/87.44	tff('262', plain,
86.84/87.44	    ~ ( g_both('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['261'])).
86.84/87.44	tff('263', plain,
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('264', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, '#sk4'(X1))
86.84/87.44	       | ~ g_both(X1, X2)
86.84/87.44	       | ~ g_false_only(X1, '#sk1')
86.84/87.44	       |  g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['157'])).
86.84/87.44	tff('265', plain,
86.84/87.44	    (( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	      | ~ g_false_only('#sk6'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))
86.84/87.44	      |  g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['263', '264'])).
86.84/87.44	tff('266', plain,
86.84/87.44	    ~ ( g_both('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['265'])).
86.84/87.44	tff('267', plain, ( '#form5'('#sk1')) <= (( '#form5'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['87'])).
86.84/87.44	tff('268', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['103'])).
86.84/87.44	tff('269', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))
86.84/87.44	        |  '#form7'('#sk1')
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        |  g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  g_true_only('#sk6'('#sk1'), '#sk1')))
86.84/87.44	      <= (( '#form5'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['267', '268'])).
86.84/87.44	tff('270', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['269'])).
86.84/87.44	tff('271', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form7'(X1)
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('272', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (((??((^[Y0 : $i]:
86.84/87.44	                 ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                  (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                  (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	          (~((??((^[Y0 : $i]:
86.84/87.44	                    (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                     g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	         (!!((^[Y0 : $i]:
86.84/87.44	                (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0))))))
86.84/87.44	       | ~ '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['271'])).
86.84/87.44	tff('273', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( ((??((^[Y0 : $i]:
86.84/87.44	                ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                 (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                 (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	         (~((??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only(Y0, '#sk6'(X1)) & g_true_only('#sk6'(X1), Y0))))))))
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))
86.84/87.44	       | ~ '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['272'])).
86.84/87.44	tff('274', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ (??((^[Y0 : $i]:
86.84/87.44	                (g_true_only(Y0, '#sk6'(X1)) & g_true_only('#sk6'(X1), Y0)))))
86.84/87.44	       | ~ '#form7'(X1)
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['273'])).
86.84/87.44	tff('275', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ (g_true_only(X2, '#sk6'(X1)) & g_true_only('#sk6'(X1), X2))
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))
86.84/87.44	       | ~ '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['274'])).
86.84/87.44	tff('276', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ g_true_only('#sk6'(X1), X2)
86.84/87.44	       | ~ '#form7'(X1)
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['275'])).
86.84/87.44	tff('277', plain,
86.84/87.44	    ![X1, X2, X3]:
86.84/87.44	      ( (g_false_only(X3, '#sk6'(X1)) | g_false_only('#sk6'(X1), X3))
86.84/87.44	       | ~ '#form7'(X1)
86.84/87.44	       | ~ g_true_only('#sk6'(X1), X2)
86.84/87.44	       | ~ g_true_only(X2, '#sk6'(X1))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['276'])).
86.84/87.44	tff('278', plain,
86.84/87.44	    ![X1, X2, X3]:
86.84/87.44	      ( g_false_only(X3, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X3)
86.84/87.44	       | ~ g_true_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ g_true_only('#sk6'(X1), X2)
86.84/87.44	       | ~ '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['277'])).
86.84/87.44	tff('279', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        | ~ g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	        | ~ '#form7'('#sk1')))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['270', '278'])).
86.84/87.44	tff('280', plain,
86.84/87.44	    ~ ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( '#form7'('#sk1')) | 
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['279'])).
86.84/87.44	tff('281', plain,
86.84/87.44	    ( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('282', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only('#sk4'(X1), X1)
86.84/87.44	       | ~ g_both(X2, X1)
86.84/87.44	       | ~ g_false_only(X1, '#sk1')
86.84/87.44	       |  g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['37'])).
86.84/87.44	tff('283', plain,
86.84/87.44	    (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))
86.84/87.44	      | ~ g_false_only('#sk6'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))
86.84/87.44	      |  g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['281', '282'])).
86.84/87.44	tff('284', plain,
86.84/87.44	    ~ ( g_both('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['283'])).
86.84/87.44	tff('285', plain,
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('286', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only('#sk4'(X1), X1)
86.84/87.44	       | ~ g_both(X1, X2)
86.84/87.44	       | ~ g_false_only(X1, '#sk1')
86.84/87.44	       |  g_false_only(X2, X1)
86.84/87.44	       |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['157'])).
86.84/87.44	tff('287', plain,
86.84/87.44	    (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))
86.84/87.44	      | ~ g_false_only('#sk6'('#sk1'), '#sk1')
86.84/87.44	      |  g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))
86.84/87.44	      |  g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['285', '286'])).
86.84/87.44	tff('288', plain,
86.84/87.44	    ~ ( g_both('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['287'])).
86.84/87.44	tff('289', plain,
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['114'])).
86.84/87.44	tff('290', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (??((^[Y0 : $i]:
86.84/87.44	               ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0))))))
86.84/87.44	       | ~ '#form7'(X1)
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['273'])).
86.84/87.44	tff('291', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( ((~(g_false_only('#sk6'(X1), '#sk8'(X1))))&
86.84/87.44	         (~(g_false_only('#sk8'(X1), '#sk6'(X1))))&
86.84/87.44	         (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1))))
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))
86.84/87.44	       | ~ '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['290'])).
86.84/87.44	tff('292', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ g_false_only('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       | ~ '#form7'(X1)
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['291'])).
86.84/87.44	tff('293', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( (g_false_only(X2, '#sk6'(X1)) | g_false_only('#sk6'(X1), X2))
86.84/87.44	       | ~ '#form7'(X1)
86.84/87.44	       | ~ g_false_only('#sk6'(X1), '#sk8'(X1))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['292'])).
86.84/87.44	tff('294', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       | ~ g_false_only('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       | ~ '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['293'])).
86.84/87.44	tff('295', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        | ~ '#form7'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['289', '294'])).
86.84/87.44	tff('296', plain,
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ~ ( '#form7'('#sk1')) | 
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['295'])).
86.84/87.44	tff('297', plain, ( '#form7'('#sk1')) <= (( '#form7'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['105'])).
86.84/87.44	tff('298', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1)))
86.84/87.44	       | ~ '#form7'(X1)
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['291'])).
86.84/87.44	tff('299', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( g_both('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       |  g_both('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))
86.84/87.44	       | ~ '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['298'])).
86.84/87.44	tff('300', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( (g_false_only(X2, '#sk6'(X1)) | g_false_only('#sk6'(X1), X2))
86.84/87.44	       | ~ '#form7'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       |  g_both('#sk8'(X1), '#sk6'(X1))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['299'])).
86.84/87.44	tff('301', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_both('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       |  g_both('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       | ~ '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['300'])).
86.84/87.44	tff('302', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        |  g_both('#sk8'('#sk1'), '#sk6'('#sk1'))
86.84/87.44	        |  g_both('#sk6'('#sk1'), '#sk8'('#sk1'))))
86.84/87.44	      <= (( '#form7'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['297', '301'])).
86.84/87.44	tff('303', plain,
86.84/87.44	    ( g_both('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( '#form7'('#sk1')), inference('split', [status(esa)], ['302'])).
86.84/87.44	tff('304', plain,
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('305', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_both(X1, X2)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')
86.84/87.44	       |  g_true_only('#sk4'(X1), X1)
86.84/87.44	       |  g_false_only(X1, X2)
86.84/87.44	       |  g_false_only(X2, X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['137'])).
86.84/87.44	tff('306', plain,
86.84/87.44	    ((~ g_true_only('#sk6'('#sk1'), '#sk1')
86.84/87.44	      |  g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))
86.84/87.44	      |  g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))
86.84/87.44	      |  g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['304', '305'])).
86.84/87.44	tff('307', plain,
86.84/87.44	    ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['306'])).
86.84/87.44	tff('308', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( g_true_only('#sk6'(X1), X1)
86.84/87.44	       |  (g_false_only('#sk6'(X1), X1) &
86.84/87.44	           (((??((^[Y0 : $i]:
86.84/87.44	                    ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                     (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                     (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	             (~((??((^[Y0 : $i]:
86.84/87.44	                       (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                        g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	            (!!((^[Y0 : $i]:
86.84/87.44	                   (g_false_only(Y0, '#sk6'(X1)) |
86.84/87.44	                    g_false_only('#sk6'(X1), Y0)))))))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['97'])).
86.84/87.44	tff('309', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (((??((^[Y0 : $i]:
86.84/87.44	                 ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                  (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                  (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	          (~((??((^[Y0 : $i]:
86.84/87.44	                    (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                     g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	         (!!((^[Y0 : $i]:
86.84/87.44	                (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0))))))
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['308'])).
86.84/87.44	tff('310', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( ((??((^[Y0 : $i]:
86.84/87.44	                ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                 (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                 (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	         (~((??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only(Y0, '#sk6'(X1)) & g_true_only('#sk6'(X1), Y0))))))))
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['309'])).
86.84/87.44	tff('311', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (??((^[Y0 : $i]:
86.84/87.44	               ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0))))))
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['310'])).
86.84/87.44	tff('312', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( ((~(g_false_only('#sk6'(X1), '#sk8'(X1))))&
86.84/87.44	         (~(g_false_only('#sk8'(X1), '#sk6'(X1))))&
86.84/87.44	         (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1))))
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['311'])).
86.84/87.44	tff('313', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ g_false_only('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['312'])).
86.84/87.44	tff('314', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( (g_false_only(X2, '#sk6'(X1)) | g_false_only('#sk6'(X1), X2))
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ g_false_only('#sk8'(X1), '#sk6'(X1))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['313'])).
86.84/87.44	tff('315', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       | ~ g_false_only('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['314'])).
86.84/87.44	tff('316', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        |  g_both('#sk6'('#sk1'), '#sk1')
86.84/87.44	        | ~ '#form5'('#sk1')
86.84/87.44	        |  g_true_only('#sk6'('#sk1'), '#sk1')))
86.84/87.44	      <= (( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['307', '315'])).
86.84/87.44	tff('317', plain,
86.84/87.44	    ~ ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk1')) | ~ ( '#form5'('#sk1')) | 
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))) | 
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['316'])).
86.84/87.44	tff('318', plain,
86.84/87.44	    ~ ( g_both('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( g_true_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['306'])).
86.84/87.44	tff('319', plain,
86.84/87.44	    ( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('320', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_both(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')
86.84/87.44	       |  g_true_only('#sk4'(X1), X1)
86.84/87.44	       |  g_false_only(X1, X2)
86.84/87.44	       |  g_false_only(X2, X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['137'])).
86.84/87.44	tff('321', plain,
86.84/87.44	    ((~ g_true_only('#sk6'('#sk1'), '#sk1')
86.84/87.44	      |  g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))
86.84/87.44	      |  g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))
86.84/87.44	      |  g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['319', '320'])).
86.84/87.44	tff('322', plain,
86.84/87.44	    ~ ( g_both('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( g_true_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['321'])).
86.84/87.44	tff('323', plain,
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('324', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_both(X1, X2)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')
86.84/87.44	       |  g_true_only(X1, '#sk4'(X1))
86.84/87.44	       |  g_false_only(X1, X2)
86.84/87.44	       |  g_false_only(X2, X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['130'])).
86.84/87.44	tff('325', plain,
86.84/87.44	    ((~ g_true_only('#sk6'('#sk1'), '#sk1')
86.84/87.44	      |  g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	      |  g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))
86.84/87.44	      |  g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['323', '324'])).
86.84/87.44	tff('326', plain,
86.84/87.44	    ~ ( g_both('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.44	    ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( g_true_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['325'])).
86.84/87.44	tff('327', plain,
86.84/87.44	    ( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('328', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_both(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')
86.84/87.44	       |  g_true_only(X1, '#sk4'(X1))
86.84/87.44	       |  g_false_only(X1, X2)
86.84/87.44	       |  g_false_only(X2, X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['130'])).
86.84/87.44	tff('329', plain,
86.84/87.44	    ((~ g_true_only('#sk6'('#sk1'), '#sk1')
86.84/87.44	      |  g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	      |  g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))
86.84/87.44	      |  g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['327', '328'])).
86.84/87.44	tff('330', plain,
86.84/87.44	    ~ ( g_both('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( g_true_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.44	    ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['329'])).
86.84/87.44	tff('331', plain,
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( '#form5'('#sk1')) | ( '#form7'('#sk1')) | 
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_both('#sk8'('#sk1'), '#sk6'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('332', plain,
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['114'])).
86.84/87.44	tff('333', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( (((??((^[Y0 : $i]:
86.84/87.44	                 ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                  (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                  (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	          (~((??((^[Y0 : $i]:
86.84/87.44	                    (g_true_only(Y0, '#sk6'(X1)) &
86.84/87.44	                     g_true_only('#sk6'(X1), Y0)))))))) |
86.84/87.44	         (??((^[Y0 : $i]:
86.84/87.44	                (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1)))))))
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['102'])).
86.84/87.44	tff('334', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( ((??((^[Y0 : $i]:
86.84/87.44	                ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                 (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                 (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0)))))) &
86.84/87.44	         (~((??((^[Y0 : $i]:
86.84/87.44	                   (g_true_only(Y0, '#sk6'(X1)) & g_true_only('#sk6'(X1), Y0))))))))
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['333'])).
86.84/87.44	tff('335', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( (??((^[Y0 : $i]:
86.84/87.44	               ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0))))))
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['334'])).
86.84/87.44	tff('336', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( ((~(g_false_only('#sk6'(X1), '#sk8'(X1))))&
86.84/87.44	         (~(g_false_only('#sk8'(X1), '#sk6'(X1))))&
86.84/87.44	         (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1))))
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['335'])).
86.84/87.44	tff('337', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_false_only('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['336'])).
86.84/87.44	tff('338', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_false_only('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['336'])).
86.84/87.44	tff('339', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form11'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('340', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( '#form11'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       | ~ g_false_only('#sk6'(X1), '#sk8'(X1))),
86.84/87.44	    inference('renaming', [status(thm)], ['337', '339'])).
86.84/87.44	tff('341', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ (??((^[Y0 : $i]:
86.84/87.44	                (g_true_only(Y0, '#sk6'(X1)) & g_true_only('#sk6'(X1), Y0)))))
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['334'])).
86.84/87.44	tff('342', plain,
86.84/87.44	    ![X1, X2, X3]:
86.84/87.44	      (~ (g_true_only(X3, '#sk6'(X1)) & g_true_only('#sk6'(X1), X3))
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['341'])).
86.84/87.44	tff('343', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form10'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('344', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( '#form10'(X1)
86.84/87.44	       | ~ g_false_only('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  '#form11'(X1)),
86.84/87.44	    inference('renaming', [status(thm)], ['340', '343'])).
86.84/87.44	tff('345', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( '#form10'('#sk1')
86.84/87.44	        | ~ '#form5'('#sk1')
86.84/87.44	        |  g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        |  '#form7'('#sk1')
86.84/87.44	        |  '#form11'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['332', '344'])).
86.84/87.44	tff('346', plain,
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( '#form7'('#sk1')) | ~ ( '#form5'('#sk1')) | 
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))) | 
86.84/87.44	    ( '#form10'('#sk1')) | ( '#form11'('#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['345'])).
86.84/87.44	tff('347', plain,
86.84/87.44	    ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['306'])).
86.84/87.44	tff('348', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_false_only('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['336'])).
86.84/87.44	tff('349', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form11'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('350', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( '#form11'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       | ~ g_false_only('#sk8'(X1), '#sk6'(X1))),
86.84/87.44	    inference('renaming', [status(thm)], ['348', '349'])).
86.84/87.44	tff('351', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form10'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('352', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( '#form10'(X1)
86.84/87.44	       | ~ g_false_only('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  '#form11'(X1)),
86.84/87.44	    inference('renaming', [status(thm)], ['350', '351'])).
86.84/87.44	tff('353', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( '#form10'('#sk1')
86.84/87.44	        | ~ '#form5'('#sk1')
86.84/87.44	        |  g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        |  '#form7'('#sk1')
86.84/87.44	        |  '#form11'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['347', '352'])).
86.84/87.44	tff('354', plain,
86.84/87.44	    ~ ( g_false_only('#sk8'('#sk1'), '#sk6'('#sk1'))) | 
86.84/87.44	    ( '#form7'('#sk1')) | ~ ( '#form5'('#sk1')) | 
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))) | 
86.84/87.44	    ( '#form10'('#sk1')) | ( '#form11'('#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['353'])).
86.84/87.44	tff('355', plain,
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_true_only('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['105'])).
86.84/87.44	tff('356', plain, ( '#form5'('#sk1')) <= (( '#form5'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['87'])).
86.84/87.44	tff('357', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1)))
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['336'])).
86.84/87.44	tff('358', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form11'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('359', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( '#form11'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1)))),
86.84/87.44	    inference('renaming', [status(thm)], ['357', '358'])).
86.84/87.44	tff('360', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form10'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('361', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( '#form10'(X1)
86.84/87.44	       |  (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  '#form11'(X1)),
86.84/87.44	    inference('renaming', [status(thm)], ['359', '360'])).
86.84/87.44	tff('362', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_both('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       |  g_both('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       |  '#form11'(X1)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  '#form10'(X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['361'])).
86.84/87.44	tff('363', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_both('#sk8'('#sk1'), '#sk6'('#sk1'))
86.84/87.44	        |  g_both('#sk6'('#sk1'), '#sk8'('#sk1'))
86.84/87.44	        |  '#form11'('#sk1')
86.84/87.44	        |  '#form7'('#sk1')
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        |  g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  '#form10'('#sk1')))
86.84/87.44	      <= (( '#form5'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['356', '362'])).
86.84/87.44	tff('364', plain, ( '#form11'('#sk1')) <= (( '#form11'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['363'])).
86.84/87.44	tff('365', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form11'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('366', plain,
86.84/87.44	    ![X1]: ( g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)) | ~ '#form11'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['365'])).
86.84/87.44	tff('367', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))
86.84/87.44	      <= (( '#form11'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['364', '366'])).
86.84/87.44	tff('368', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, X2)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['174'])).
86.84/87.44	tff('369', plain,
86.84/87.44	    ((~ g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	      | ~ g_true_only('#sk6'('#sk1'), '#sk1'))) <= (( '#form11'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['367', '368'])).
86.84/87.44	tff('370', plain, ( '#form11'('#sk1')) <= (( '#form11'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['363'])).
86.84/87.44	tff('371', plain,
86.84/87.44	    ![X1]: ( g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) | ~ '#form11'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['365'])).
86.84/87.44	tff('372', plain,
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1'))))
86.84/87.44	      <= (( '#form11'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['370', '371'])).
86.84/87.44	tff('373', plain,
86.84/87.44	    (~ g_true_only('#sk6'('#sk1'), '#sk1')) <= (( '#form11'('#sk1'))),
86.84/87.44	    inference('demod', [status(thm)], ['369', '372'])).
86.84/87.44	tff('374', plain,
86.84/87.44	    ~ ( '#form11'('#sk1')) | ~ ( g_true_only('#sk6'('#sk1'), '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['355', '373'])).
86.84/87.44	tff('375', plain,
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_true_only('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['105'])).
86.84/87.44	tff('376', plain, ( '#form10'('#sk1')) <= (( '#form10'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['363'])).
86.84/87.44	tff('377', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form10'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('378', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	         g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form10'(X1)),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['377'])).
86.84/87.44	tff('379', plain,
86.84/87.44	    ![X1]: ( g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)) | ~ '#form10'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['378'])).
86.84/87.44	tff('380', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))
86.84/87.44	      <= (( '#form10'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['376', '379'])).
86.84/87.44	tff('381', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, X2)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['174'])).
86.84/87.44	tff('382', plain,
86.84/87.44	    ((~ g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	      | ~ g_true_only('#sk6'('#sk1'), '#sk1'))) <= (( '#form10'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['380', '381'])).
86.84/87.44	tff('383', plain, ( '#form10'('#sk1')) <= (( '#form10'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['363'])).
86.84/87.44	tff('384', plain,
86.84/87.44	    ![X1]: ( g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) | ~ '#form10'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['378'])).
86.84/87.44	tff('385', plain,
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1'))))
86.84/87.44	      <= (( '#form10'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['383', '384'])).
86.84/87.44	tff('386', plain,
86.84/87.44	    (~ g_true_only('#sk6'('#sk1'), '#sk1')) <= (( '#form10'('#sk1'))),
86.84/87.44	    inference('demod', [status(thm)], ['382', '385'])).
86.84/87.44	tff('387', plain,
86.84/87.44	    ~ ( '#form10'('#sk1')) | ~ ( g_true_only('#sk6'('#sk1'), '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['375', '386'])).
86.84/87.44	tff('388', plain, ( '#form5'('#sk1')) <= (( '#form5'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['87'])).
86.84/87.44	tff('389', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 ((~(g_false_only('#sk6'(X1), Y0)))&
86.84/87.44	                  (~(g_false_only(Y0, '#sk6'(X1))))&
86.84/87.44	                  (g_both(Y0, '#sk6'(X1)) | g_both('#sk6'(X1), Y0))))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['110'])).
86.84/87.44	tff('390', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( ((~(g_false_only('#sk6'(X1), '#sk8'(X1))))&
86.84/87.44	         (~(g_false_only('#sk8'(X1), '#sk6'(X1))))&
86.84/87.44	         (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1))))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1))),
86.84/87.44	    inference('lazy_cnf_exists', [status(thm)], ['389'])).
86.84/87.44	tff('391', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( (g_both('#sk8'(X1), '#sk6'(X1)) | g_both('#sk6'(X1), '#sk8'(X1)))
86.84/87.44	       |  g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['390'])).
86.84/87.44	tff('392', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      ( g_both('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       |  g_both('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1))),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['391'])).
86.84/87.44	tff('393', plain,
86.84/87.44	    (( g_both('#sk8'('#sk1'), '#sk6'('#sk1'))
86.84/87.44	      |  g_both('#sk6'('#sk1'), '#sk8'('#sk1'))
86.84/87.44	      |  g_both('#sk6'('#sk1'), '#sk1')
86.84/87.44	      |  '#form7'('#sk1')
86.84/87.44	      |  g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))))
86.84/87.44	      <= (( '#form5'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['388', '392'])).
86.84/87.44	tff('394', plain,
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( '#form5'('#sk1')) | ( '#form7'('#sk1')) | 
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_both('#sk8'('#sk1'), '#sk6'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['393'])).
86.84/87.44	tff('395', plain,
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')) <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff(both_g, axiom,
86.84/87.44	  (![X_2,X_1]: ((g_true(X_2,X_1) & g_false(X_2,X_1)) <=> g_both(X_2,X_1)))).
86.84/87.44	tff('396', plain,
86.84/87.44	     (!!((^[Y0 : $i]:
86.84/87.44	            (!!((^[Y1 : $i]:
86.84/87.44	                   ((g_true(Y0, Y1) & g_false(Y0, Y1)) <=> g_both(Y0, Y1)))))))),
86.84/87.44	    inference('cnf', [status(esa)], [both_g])).
86.84/87.44	tff('397', plain,
86.84/87.44	    ![X1]:
86.84/87.44	       (!!((^[Y0 : $i]:
86.84/87.44	              ((g_true(X1, Y0) & g_false(X1, Y0)) <=> g_both(X1, Y0))))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['396'])).
86.84/87.44	tff('398', plain,
86.84/87.44	    ![X1, X2]:  ((g_true(X1, X2) & g_false(X1, X2)) <=> g_both(X1, X2)),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['397'])).
86.84/87.44	tff('399', plain,
86.84/87.44	    ( ((g_true('#sk6'('#sk1'), '#sk1') & g_false('#sk6'('#sk1'), '#sk1')) <=>
86.84/87.44	       $true))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup+', [status(thm)], ['395', '398'])).
86.84/87.44	tff('400', plain,
86.84/87.44	    ( (g_true('#sk6'('#sk1'), '#sk1') & g_false('#sk6'('#sk1'), '#sk1')))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('lazy_cnf_equiv', [status(thm)], ['399'])).
86.84/87.44	tff('401', plain,
86.84/87.44	    ( g_false('#sk6'('#sk1'), '#sk1')) <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['400'])).
86.84/87.44	tff('402', plain,
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_true_only('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['105'])).
86.84/87.44	tff(true_only_g, axiom,
86.84/87.44	  (![X_2,X_1]:
86.84/87.44	     (g_true_only(X_2,X_1) <=> (g_true(X_2,X_1) & (~g_false(X_2,X_1)))))).
86.84/87.44	tff('403', plain,
86.84/87.44	     (!!((^[Y0 : $i]:
86.84/87.44	            (!!((^[Y1 : $i]:
86.84/87.44	                   (g_true_only(Y0, Y1) <=>
86.84/87.44	                    (g_true(Y0, Y1) & (~(g_false(Y0, Y1))))))))))),
86.84/87.44	    inference('cnf', [status(esa)], [true_only_g])).
86.84/87.44	tff('404', plain,
86.84/87.44	    ![X1]:
86.84/87.44	       (!!((^[Y0 : $i]:
86.84/87.44	              (g_true_only(X1, Y0) <=>
86.84/87.44	               (g_true(X1, Y0) & (~(g_false(X1, Y0)))))))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['403'])).
86.84/87.44	tff('405', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	       (g_true_only(X1, X2) <=> (g_true(X1, X2) & (~(g_false(X1, X2))))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['404'])).
86.84/87.44	tff('406', plain,
86.84/87.44	    ( ($true <=>
86.84/87.44	       (g_true('#sk6'('#sk1'), '#sk1') & (~(g_false('#sk6'('#sk1'), '#sk1'))))))
86.84/87.44	      <= (( g_true_only('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup+', [status(thm)], ['402', '405'])).
86.84/87.44	tff('407', plain,
86.84/87.44	    ( (g_true('#sk6'('#sk1'), '#sk1') & (~(g_false('#sk6'('#sk1'), '#sk1')))))
86.84/87.44	      <= (( g_true_only('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('lazy_cnf_equiv', [status(thm)], ['406'])).
86.84/87.44	tff('408', plain,
86.84/87.44	    (~ g_false('#sk6'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_true_only('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['407'])).
86.84/87.44	tff('409', plain,
86.84/87.44	    ~ ( g_both('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_true_only('#sk6'('#sk1'), '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['401', '408'])).
86.84/87.44	tff('410', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))
86.84/87.44	      <= (( '#form10'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['376', '379'])).
86.84/87.44	tff('411', plain,
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')) <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('412', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, X1) | ~ g_true_only(X1, X2) | ~ g_both(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['232'])).
86.84/87.44	tff('413', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       (~ g_true_only(X0, '#sk6'('#sk1')) | ~ g_true_only('#sk6'('#sk1'), X0)))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['411', '412'])).
86.84/87.44	tff('414', plain,
86.84/87.44	    (~ g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk1')) & ( '#form10'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['410', '413'])).
86.84/87.44	tff('415', plain,
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1'))))
86.84/87.44	      <= (( '#form10'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['383', '384'])).
86.84/87.44	tff('416', plain,
86.84/87.44	    ~ ( '#form10'('#sk1')) | ~ ( g_both('#sk6'('#sk1'), '#sk1')),
86.84/87.44	    inference('demod', [status(thm)], ['414', '415'])).
86.84/87.44	tff('417', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.44	    ( '#form7'('#sk1')) | ~ ( '#form5'('#sk1')) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['269'])).
86.84/87.44	tff('418', plain,
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.44	    ( '#form7'('#sk1')) | ~ ( '#form5'('#sk1')) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['105'])).
86.84/87.44	tff('419', plain,
86.84/87.44	    ( g_true('#sk6'('#sk1'), '#sk1')) <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['400'])).
86.84/87.44	tff('420', plain, ( '#form7'('#sk1')) <= (( '#form7'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['105'])).
86.84/87.44	tff('421', plain, ![X1]: ( g_false_only('#sk6'(X1), X1) | ~ '#form7'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['271'])).
86.84/87.44	tff('422', plain,
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk1')) <= (( '#form7'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['420', '421'])).
86.84/87.44	tff(false_only_g, axiom,
86.84/87.44	  (![X_2,X_1]:
86.84/87.44	     (g_false_only(X_2,X_1) <=> (g_false(X_2,X_1) & (~g_true(X_2,X_1)))))).
86.84/87.44	tff('423', plain,
86.84/87.44	     (!!((^[Y0 : $i]:
86.84/87.44	            (!!((^[Y1 : $i]:
86.84/87.44	                   (g_false_only(Y0, Y1) <=>
86.84/87.44	                    (g_false(Y0, Y1) & (~(g_true(Y0, Y1))))))))))),
86.84/87.44	    inference('cnf', [status(esa)], [false_only_g])).
86.84/87.44	tff('424', plain,
86.84/87.44	    ![X1]:
86.84/87.44	       (!!((^[Y0 : $i]:
86.84/87.44	              (g_false_only(X1, Y0) <=>
86.84/87.44	               (g_false(X1, Y0) & (~(g_true(X1, Y0)))))))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['423'])).
86.84/87.44	tff('425', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	       (g_false_only(X1, X2) <=> (g_false(X1, X2) & (~(g_true(X1, X2))))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['424'])).
86.84/87.44	tff('426', plain,
86.84/87.44	    ( ($true <=>
86.84/87.44	       (g_false('#sk6'('#sk1'), '#sk1') & (~(g_true('#sk6'('#sk1'), '#sk1'))))))
86.84/87.44	      <= (( '#form7'('#sk1'))),
86.84/87.44	    inference('s_sup+', [status(thm)], ['422', '425'])).
86.84/87.44	tff('427', plain,
86.84/87.44	    ( (g_false('#sk6'('#sk1'), '#sk1') & (~(g_true('#sk6'('#sk1'), '#sk1')))))
86.84/87.44	      <= (( '#form7'('#sk1'))),
86.84/87.44	    inference('lazy_cnf_equiv', [status(thm)], ['426'])).
86.84/87.44	tff('428', plain,
86.84/87.44	    (~ g_true('#sk6'('#sk1'), '#sk1')) <= (( '#form7'('#sk1'))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['427'])).
86.84/87.44	tff('429', plain,
86.84/87.44	    ~ ( g_both('#sk6'('#sk1'), '#sk1')) | ~ ( '#form7'('#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['419', '428'])).
86.84/87.44	tff('430', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))
86.84/87.44	      <= (( '#form11'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['364', '366'])).
86.84/87.44	tff('431', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       (~ g_true_only(X0, '#sk6'('#sk1')) | ~ g_true_only('#sk6'('#sk1'), X0)))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['411', '412'])).
86.84/87.44	tff('432', plain,
86.84/87.44	    (~ g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk1')) & ( '#form11'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['430', '431'])).
86.84/87.44	tff('433', plain,
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1'))))
86.84/87.44	      <= (( '#form11'('#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['370', '371'])).
86.84/87.44	tff('434', plain,
86.84/87.44	    ~ ( '#form11'('#sk1')) | ~ ( g_both('#sk6'('#sk1'), '#sk1')),
86.84/87.44	    inference('demod', [status(thm)], ['432', '433'])).
86.84/87.44	tff('435', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['269'])).
86.84/87.44	tff('436', plain,
86.84/87.44	    ![X1, X2, X3]:
86.84/87.44	      (~ (g_true_only(X3, '#sk6'(X1)) & g_true_only('#sk6'(X1), X3))
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['341'])).
86.84/87.44	tff('437', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form10'(X1)
86.84/87.44	       |  (??((^[Y0 : $i]:
86.84/87.44	                 (g_true_only('#sk6'(X1), Y0) & g_true_only(Y0, '#sk6'(X1))))))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('438', plain,
86.84/87.44	    ![X1, X2, X3]:
86.84/87.44	      ( '#form10'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       | ~ (g_true_only(X3, '#sk6'(X1)) & g_true_only('#sk6'(X1), X3))),
86.84/87.44	    inference('renaming', [status(thm)], ['436', '437'])).
86.84/87.44	tff('439', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ '#form11'(X1)
86.84/87.44	       |  (g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1))) &
86.84/87.44	           g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1)))),
86.84/87.44	    define([status(thm)])).
86.84/87.44	tff('440', plain,
86.84/87.44	    ![X1, X2, X3]:
86.84/87.44	      ( '#form11'(X1)
86.84/87.44	       | ~ (g_true_only(X3, '#sk6'(X1)) & g_true_only('#sk6'(X1), X3))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  '#form10'(X1)),
86.84/87.44	    inference('renaming', [status(thm)], ['438', '439'])).
86.84/87.44	tff('441', plain,
86.84/87.44	    ![X1, X2, X3]:
86.84/87.44	      (~ g_true_only(X3, '#sk6'(X1))
86.84/87.44	       | ~ g_true_only('#sk6'(X1), X3)
86.84/87.44	       |  '#form10'(X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_false_only(X2, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X2)
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  '#form11'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['440'])).
86.84/87.44	tff('442', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       (~ g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	        |  '#form10'('#sk1')
86.84/87.44	        | ~ '#form5'('#sk1')
86.84/87.44	        |  g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        |  '#form7'('#sk1')
86.84/87.44	        |  '#form11'('#sk1')))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['435', '441'])).
86.84/87.44	tff('443', plain,
86.84/87.44	    ~ ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( '#form5'('#sk1')) | ( '#form7'('#sk1')) | 
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))) | 
86.84/87.44	    ( '#form10'('#sk1')) | ( '#form11'('#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['442'])).
86.84/87.44	tff('444', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.44	tff('445', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1'))))
86.84/87.44	      <= ((![X0]:
86.84/87.44	             ( g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	              |  g_false_only(X0, '#sk6'('#sk1'))))),
86.84/87.44	    inference('split', [status(esa)], ['105'])).
86.84/87.44	tff('446', plain,
86.84/87.44	    ![X1]: (~ g_false_only('#sk3'(X1), X1) | ~ g_false_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['26'])).
86.84/87.44	tff('447', plain,
86.84/87.44	    (( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1')))
86.84/87.44	      | ~ g_false_only('#sk6'('#sk1'), '#sk1')))
86.84/87.44	      <= ((![X0]:
86.84/87.44	             ( g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	              |  g_false_only(X0, '#sk6'('#sk1'))))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['445', '446'])).
86.84/87.44	tff('448', plain,
86.84/87.44	    (~ g_false_only('#sk6'('#sk1'), '#sk1'))
86.84/87.44	      <= (~ ( g_false_only('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['447'])).
86.84/87.44	tff('449', plain,
86.84/87.44	    (( g_both('#sk6'('#sk1'), '#sk1') |  g_true_only('#sk6'('#sk1'), '#sk1')))
86.84/87.44	      <= (~ ( g_false_only('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['444', '448'])).
86.84/87.44	tff('450', plain,
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['449'])).
86.84/87.44	tff('451', plain,
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1'))))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1'))))),
86.84/87.44	    inference('split', [status(esa)], ['447'])).
86.84/87.44	tff('452', plain,
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')) <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('453', plain,
86.84/87.44	    ![X1]: (~ g_false_only(X1, '#sk3'(X1)) | ~ g_both(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['46'])).
86.84/87.44	tff('454', plain,
86.84/87.44	    (~ g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['452', '453'])).
86.84/87.44	tff('455', plain,
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( g_both('#sk6'('#sk1'), '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['451', '454'])).
86.84/87.44	tff('456', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      ( g_true_only(X1, X2) |  g_both(X1, X2) |  g_false_only(X1, X2)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['15'])).
86.84/87.44	tff('457', plain,
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1'))))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1'))))),
86.84/87.44	    inference('split', [status(esa)], ['447'])).
86.84/87.44	tff('458', plain,
86.84/87.44	    ![X1]: (~ g_false_only(X1, '#sk3'(X1)) | ~ g_false_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['26'])).
86.84/87.44	tff('459', plain,
86.84/87.44	    (~ g_false_only('#sk6'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1'))))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['457', '458'])).
86.84/87.44	tff('460', plain,
86.84/87.44	    (( g_both('#sk6'('#sk1'), '#sk1') |  g_true_only('#sk6'('#sk1'), '#sk1')))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1'))))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['456', '459'])).
86.84/87.44	tff('461', plain,
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1')))) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')),
86.84/87.44	    inference('split', [status(esa)], ['460'])).
86.84/87.44	tff('462', plain,
86.84/87.44	    ( g_false('#sk6'('#sk1'), '#sk1')) <= (( '#form7'('#sk1'))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['427'])).
86.84/87.44	tff('463', plain,
86.84/87.44	    (~ g_false('#sk6'('#sk1'), '#sk1'))
86.84/87.44	      <= (( g_true_only('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['407'])).
86.84/87.44	tff('464', plain,
86.84/87.44	    ~ ( g_true_only('#sk6'('#sk1'), '#sk1')) | ~ ( '#form7'('#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['462', '463'])).
86.84/87.44	tff('465', plain,
86.84/87.44	    ~
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( '#form5'('#sk1')) | ( '#form7'('#sk1')) | 
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['114'])).
86.84/87.44	tff('466', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['269'])).
86.84/87.44	tff('467', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, X1)
86.84/87.44	       | ~ g_true_only(X1, X2)
86.84/87.44	       | ~ g_true_only(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['174'])).
86.84/87.44	tff('468', plain,
86.84/87.44	    ((~ g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	      | ~ g_true_only('#sk6'('#sk1'), '#sk1')))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['466', '467'])).
86.84/87.44	tff('469', plain,
86.84/87.44	    ~ ( g_true_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ~ ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['468'])).
86.84/87.44	tff('470', plain,
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['114'])).
86.84/87.44	tff('471', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ g_false_only('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       |  g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['390'])).
86.84/87.44	tff('472', plain,
86.84/87.44	    (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))
86.84/87.44	      |  '#form7'('#sk1')
86.84/87.44	      |  g_both('#sk6'('#sk1'), '#sk1')
86.84/87.44	      | ~ '#form5'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['470', '471'])).
86.84/87.44	tff('473', plain,
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( '#form5'('#sk1')) | ( g_both('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( '#form7'('#sk1')), inference('split', [status(esa)], ['472'])).
86.84/87.44	tff('474', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1'))))
86.84/87.44	      <= ((![X0]:
86.84/87.44	             ( g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	              |  g_false_only(X0, '#sk6'('#sk1'))))),
86.84/87.44	    inference('split', [status(esa)], ['105'])).
86.84/87.44	tff('475', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ g_false_only('#sk8'(X1), '#sk6'(X1))
86.84/87.44	       |  g_true_only('#sk4'('#sk6'(X1)), '#sk6'(X1))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['390'])).
86.84/87.44	tff('476', plain,
86.84/87.44	    (( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))
86.84/87.44	      |  g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))
86.84/87.44	      |  '#form7'('#sk1')
86.84/87.44	      |  g_both('#sk6'('#sk1'), '#sk1')
86.84/87.44	      | ~ '#form5'('#sk1')))
86.84/87.44	      <= ((![X0]:
86.84/87.44	             ( g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	              |  g_false_only(X0, '#sk6'('#sk1'))))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['474', '475'])).
86.84/87.44	tff('477', plain,
86.84/87.44	    ~
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))) | 
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.44	    ~ ( '#form5'('#sk1')) | ( '#form7'('#sk1')) | 
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['476'])).
86.84/87.44	tff('478', plain,
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['114'])).
86.84/87.44	tff('479', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ g_false_only('#sk6'(X1), '#sk8'(X1))
86.84/87.44	       |  g_true_only('#sk6'(X1), '#sk4'('#sk6'(X1)))
86.84/87.44	       |  '#form7'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['112'])).
86.84/87.44	tff('480', plain,
86.84/87.44	    (( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	      |  '#form7'('#sk1')
86.84/87.44	      |  g_both('#sk6'('#sk1'), '#sk1')
86.84/87.44	      | ~ '#form5'('#sk1')))
86.84/87.44	      <= (( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1')))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['478', '479'])).
86.84/87.44	tff('481', plain,
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk8'('#sk1'))) | 
86.84/87.44	    ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( '#form5'('#sk1')) | ( g_both('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( '#form7'('#sk1')), inference('split', [status(esa)], ['480'])).
86.84/87.44	tff('482', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1'))))
86.84/87.44	      <= ((![X0]:
86.84/87.44	             ( g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	              |  g_false_only(X0, '#sk6'('#sk1'))))),
86.84/87.44	    inference('split', [status(esa)], ['105'])).
86.84/87.44	tff('483', plain,
86.84/87.44	    ( g_both('#sk6'('#sk1'), '#sk1')) <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('split', [status(esa)], ['258'])).
86.84/87.44	tff('484', plain,
86.84/87.44	    ![X1]: (~ g_false_only('#sk3'(X1), X1) | ~ g_both(X1, '#sk1')),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['46'])).
86.84/87.44	tff('485', plain,
86.84/87.44	    (~ g_false_only('#sk3'('#sk6'('#sk1')), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['483', '484'])).
86.84/87.44	tff('486', plain,
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1'))))
86.84/87.44	      <= ((![X0]:
86.84/87.44	             ( g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	              |  g_false_only(X0, '#sk6'('#sk1')))) & 
86.84/87.44	          ( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['482', '485'])).
86.84/87.44	tff('487', plain,
86.84/87.44	    (~ g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1'))))
86.84/87.44	      <= (( g_both('#sk6'('#sk1'), '#sk1'))),
86.84/87.44	    inference('s_sup-', [status(thm)], ['452', '453'])).
86.84/87.44	tff('488', plain,
86.84/87.44	    ~
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( g_both('#sk6'('#sk1'), '#sk1')),
86.84/87.44	    inference('s_sup-', [status(thm)], ['486', '487'])).
86.84/87.44	tff('489', plain,
86.84/87.44	    ~
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))) | 
86.84/87.44	    ~ ( g_false_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.44	    ( g_false_only('#sk6'('#sk1'), '#sk3'('#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['447'])).
86.84/87.44	tff('490', plain,
86.84/87.44	    ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))),
86.84/87.44	    inference('split', [status(esa)], ['269'])).
86.84/87.44	tff('491', plain,
86.84/87.44	    ![X1]:
86.84/87.44	      (~ (??((^[Y0 : $i]:
86.84/87.44	                (g_true_only(Y0, '#sk6'(X1)) & g_true_only('#sk6'(X1), Y0)))))
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['310'])).
86.84/87.44	tff('492', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ (g_true_only(X2, '#sk6'(X1)) & g_true_only('#sk6'(X1), X2))
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['491'])).
86.84/87.44	tff('493', plain,
86.84/87.44	    ![X1, X2]:
86.84/87.44	      (~ g_true_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ g_true_only('#sk6'(X1), X2)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)
86.84/87.44	       |  (!!((^[Y0 : $i]:
86.84/87.44	                 (g_false_only(Y0, '#sk6'(X1)) | g_false_only('#sk6'(X1), Y0)))))),
86.84/87.44	    inference('lazy_cnf_and', [status(thm)], ['492'])).
86.84/87.44	tff('494', plain,
86.84/87.44	    ![X1, X2, X3]:
86.84/87.44	      ( (g_false_only(X3, '#sk6'(X1)) | g_false_only('#sk6'(X1), X3))
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ g_true_only('#sk6'(X1), X2)
86.84/87.44	       | ~ g_true_only(X2, '#sk6'(X1))),
86.84/87.44	    inference('lazy_cnf_forall', [status(thm)], ['493'])).
86.84/87.44	tff('495', plain,
86.84/87.44	    ![X1, X2, X3]:
86.84/87.44	      ( g_false_only(X3, '#sk6'(X1))
86.84/87.44	       |  g_false_only('#sk6'(X1), X3)
86.84/87.44	       | ~ g_true_only(X2, '#sk6'(X1))
86.84/87.44	       | ~ g_true_only('#sk6'(X1), X2)
86.84/87.44	       |  g_both('#sk6'(X1), X1)
86.84/87.44	       | ~ '#form5'(X1)
86.84/87.44	       |  g_true_only('#sk6'(X1), X1)),
86.84/87.44	    inference('lazy_cnf_or', [status(thm)], ['494'])).
86.84/87.44	tff('496', plain,
86.84/87.44	    (![X0]:
86.84/87.44	       ( g_false_only(X0, '#sk6'('#sk1'))
86.84/87.44	        |  g_false_only('#sk6'('#sk1'), X0)
86.84/87.44	        | ~ g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))
86.84/87.44	        |  g_both('#sk6'('#sk1'), '#sk1')
86.84/87.44	        | ~ '#form5'('#sk1')
86.84/87.44	        |  g_true_only('#sk6'('#sk1'), '#sk1')))
86.84/87.44	      <= (( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1')))),
86.84/87.45	    inference('s_sup-', [status(thm)], ['490', '495'])).
86.84/87.45	tff('497', plain,
86.84/87.45	    ~ ( g_true_only('#sk6'('#sk1'), '#sk4'('#sk6'('#sk1')))) | 
86.84/87.45	    ~ ( g_true_only('#sk4'('#sk6'('#sk1')), '#sk6'('#sk1'))) | 
86.84/87.45	    ~ ( '#form5'('#sk1')) | ( g_true_only('#sk6'('#sk1'), '#sk1')) | 
86.84/87.45	    ( g_both('#sk6'('#sk1'), '#sk1')) | 
86.84/87.45	    (![X0]:
86.84/87.45	       ( g_false_only('#sk6'('#sk1'), X0) |  g_false_only(X0, '#sk6'('#sk1')))),
86.84/87.45	    inference('split', [status(esa)], ['496'])).
86.84/87.45	tff('498', plain,
86.84/87.45	    ~ ( g_true_only('#sk4'('#sk1'), '#sk1')) | 
86.84/87.45	    ~ ( g_true_only('#sk1', '#sk4'('#sk1'))),
86.84/87.45	    inference('s_sup-', [status(thm)], ['168', '177'])).
86.84/87.45	tff('499', plain,
86.84/87.45	    ~ ( g_false_only('#sk1', '#sk1')) | 
86.84/87.45	    ( g_true_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.45	    ( g_both('#sk1', '#sk3'('#sk1'))),
86.84/87.45	    inference('split', [status(esa)], ['192'])).
86.84/87.45	tff('500', plain, ( g_both('#sk1', '#sk1')) <= (( g_both('#sk1', '#sk1'))),
86.84/87.45	    inference('split', [status(esa)], ['206'])).
86.84/87.45	tff('501', plain, ( g_both('#sk1', '#sk1')),
86.84/87.45	    inference('sat_resolution*', [status(thm)],
86.84/87.45	              ['160', '164', '178', '187', '193', '197', '201', '207', 
86.84/87.45	               '213', '214', '217', '223'])).
86.84/87.45	tff('502', plain,  g_both('#sk1', '#sk1'),
86.84/87.45	    inference('simpl_trail', [status(thm)], ['500', '501'])).
86.84/87.45	tff('503', plain,
86.84/87.45	    (![X0]:
86.84/87.45	       ( g_false_only(X0, '#sk1')
86.84/87.45	        |  g_false_only('#sk1', X0)
86.84/87.45	        | ~ g_both('#sk1', X0)))
86.84/87.45	      <= ((![X0]:
86.84/87.45	             ( g_false_only(X0, '#sk1')
86.84/87.45	              |  g_false_only('#sk1', X0)
86.84/87.45	              | ~ g_both('#sk1', X0)))),
86.84/87.45	    inference('split', [status(esa)], ['87'])).
86.84/87.45	tff('504', plain,
86.84/87.45	    (( g_false_only('#sk1', '#sk1') |  g_false_only('#sk1', '#sk1')))
86.84/87.45	      <= ((![X0]:
86.84/87.45	             ( g_false_only(X0, '#sk1')
86.84/87.45	              |  g_false_only('#sk1', X0)
86.84/87.45	              | ~ g_both('#sk1', X0)))),
86.84/87.45	    inference('s_sup-', [status(thm)], ['502', '503'])).
86.84/87.45	tff('505', plain,
86.84/87.45	    ( g_false_only('#sk1', '#sk1'))
86.84/87.45	      <= ((![X0]:
86.84/87.45	             ( g_false_only(X0, '#sk1')
86.84/87.45	              |  g_false_only('#sk1', X0)
86.84/87.45	              | ~ g_both('#sk1', X0)))),
86.84/87.45	    inference('simplify', [status(thm)], ['504'])).
86.84/87.45	tff('506', plain,
86.84/87.45	    ![X0]:
86.84/87.45	      ( g_both('#sk3'(X0), X0)
86.84/87.45	       |  g_true_only('#sk3'(X0), X0)
86.84/87.45	       | ~ g_false_only(X0, '#sk1')),
86.84/87.45	    inference('s_sup-', [status(thm)], ['183', '184'])).
86.84/87.45	tff('507', plain,
86.84/87.45	    (( g_both('#sk3'('#sk1'), '#sk1') |  g_true_only('#sk3'('#sk1'), '#sk1')))
86.84/87.45	      <= ((![X0]:
86.84/87.45	             ( g_false_only(X0, '#sk1')
86.84/87.45	              |  g_false_only('#sk1', X0)
86.84/87.45	              | ~ g_both('#sk1', X0)))),
86.84/87.45	    inference('s_sup-', [status(thm)], ['505', '506'])).
86.84/87.45	tff('508', plain,
86.84/87.45	    ( g_both('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.45	    inference('split', [status(esa)], ['507'])).
86.84/87.45	tff('509', plain, ( g_both('#sk3'('#sk1'), '#sk1')),
86.84/87.45	    inference('sat_resolution*', [status(thm)],
86.84/87.45	              ['133', '140', '146', '152', '227', '236', '237', '238', 
86.84/87.45	               '178', '187', '239', '240', '241', '207', '213', '214', 
86.84/87.45	               '217', '223', '248', '249'])).
86.84/87.45	tff('510', plain,  g_both('#sk3'('#sk1'), '#sk1'),
86.84/87.45	    inference('simpl_trail', [status(thm)], ['508', '509'])).
86.84/87.45	tff('511', plain,
86.84/87.45	    ( g_both('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.45	    inference('split', [status(esa)], ['61'])).
86.84/87.45	tff('512', plain,
86.84/87.45	    (![X1, X2, X3]:
86.84/87.45	       ( '#form5'(X1)
86.84/87.45	        |  g_false_only(X3, X2)
86.84/87.45	        |  g_false_only(X2, X3)
86.84/87.45	        |  g_true_only(X2, '#sk4'(X2))
86.84/87.45	        | ~ g_both(X2, X1)
86.84/87.45	        | ~ g_both(X2, X3)))
86.84/87.45	      <= (~
86.84/87.45	          ( (??((^[Y0 : $i]:
86.84/87.45	                   ((??((^[Y1 : $i]:
86.84/87.45	                           ((~((??((^[Y2 : $i]:
86.84/87.45	                                      (g_true_only(Y1, Y2) &
86.84/87.45	                                       g_true_only(Y2, Y1)))))))&
86.84/87.45	                            (??((^[Y2 : $i]:
86.84/87.45	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.45	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.45	                            g_both(Y1, Y0))))) &
86.84/87.45	                    (~((??((^[Y1 : $i]:
86.84/87.45	                              ((((!!((^[Y2 : $i]:
86.84/87.45	                                        (g_false_only(Y1, Y2) |
86.84/87.45	                                         g_false_only(Y2, Y1))))) |
86.84/87.45	                                 (??((^[Y2 : $i]:
86.84/87.45	                                        (g_true_only(Y1, Y2) &
86.84/87.45	                                         g_true_only(Y2, Y1)))))) &
86.84/87.45	                                g_both(Y1, Y0))|
86.84/87.45	                               (g_false_only(Y1, Y0) &
86.84/87.45	                                (((??((^[Y2 : $i]:
86.84/87.45	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.45	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.45	                                  (~((??((^[Y2 : $i]:
86.84/87.45	                                            (g_true_only(Y2, Y1) &
86.84/87.45	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.45	                                 (!!((^[Y2 : $i]:
86.84/87.45	                                        (g_false_only(Y2, Y1) |
86.84/87.45	                                         g_false_only(Y1, Y2)))))))|
86.84/87.45	                               ((((??((^[Y2 : $i]:
86.84/87.45	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.45	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.45	                                  (~((??((^[Y2 : $i]:
86.84/87.45	                                            (g_true_only(Y2, Y1) &
86.84/87.45	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.45	                                 (??((^[Y2 : $i]:
86.84/87.45	                                        (g_true_only(Y1, Y2) &
86.84/87.45	                                         g_true_only(Y2, Y1)))))) &
86.84/87.45	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.45	    inference('renaming', [status(thm)], ['84', '85'])).
86.84/87.45	tff('513', plain,
86.84/87.45	    (![X0]:
86.84/87.45	       ( '#form5'('#sk1')
86.84/87.45	        |  g_false_only(X0, '#sk3'('#sk1'))
86.84/87.45	        |  g_false_only('#sk3'('#sk1'), X0)
86.84/87.45	        |  g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))
86.84/87.45	        | ~ g_both('#sk3'('#sk1'), X0)))
86.84/87.45	      <= (~
86.84/87.45	          ( (??((^[Y0 : $i]:
86.84/87.45	                   ((??((^[Y1 : $i]:
86.84/87.45	                           ((~((??((^[Y2 : $i]:
86.84/87.45	                                      (g_true_only(Y1, Y2) &
86.84/87.45	                                       g_true_only(Y2, Y1)))))))&
86.84/87.45	                            (??((^[Y2 : $i]:
86.84/87.45	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.45	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.45	                            g_both(Y1, Y0))))) &
86.84/87.45	                    (~((??((^[Y1 : $i]:
86.84/87.45	                              ((((!!((^[Y2 : $i]:
86.84/87.45	                                        (g_false_only(Y1, Y2) |
86.84/87.45	                                         g_false_only(Y2, Y1))))) |
86.84/87.45	                                 (??((^[Y2 : $i]:
86.84/87.45	                                        (g_true_only(Y1, Y2) &
86.84/87.45	                                         g_true_only(Y2, Y1)))))) &
86.84/87.45	                                g_both(Y1, Y0))|
86.84/87.45	                               (g_false_only(Y1, Y0) &
86.84/87.45	                                (((??((^[Y2 : $i]:
86.84/87.45	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.45	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.45	                                  (~((??((^[Y2 : $i]:
86.84/87.45	                                            (g_true_only(Y2, Y1) &
86.84/87.45	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.45	                                 (!!((^[Y2 : $i]:
86.84/87.45	                                        (g_false_only(Y2, Y1) |
86.84/87.45	                                         g_false_only(Y1, Y2)))))))|
86.84/87.45	                               ((((??((^[Y2 : $i]:
86.84/87.45	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.45	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.45	                                  (~((??((^[Y2 : $i]:
86.84/87.45	                                            (g_true_only(Y2, Y1) &
86.84/87.45	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.45	                                 (??((^[Y2 : $i]:
86.84/87.45	                                        (g_true_only(Y1, Y2) &
86.84/87.45	                                         g_true_only(Y2, Y1)))))) &
86.84/87.45	                                g_true_only(Y1, Y0))))))))))))) & 
86.84/87.45	          ( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.45	    inference('s_sup-', [status(thm)], ['511', '512'])).
86.84/87.45	tff('514', plain,
86.84/87.45	    (![X0]:
86.84/87.45	       ( g_false_only(X0, '#sk3'('#sk1'))
86.84/87.45	        |  g_false_only('#sk3'('#sk1'), X0)
86.84/87.45	        | ~ g_both('#sk3'('#sk1'), X0)))
86.84/87.45	      <= ((![X0]:
86.84/87.45	             ( g_false_only(X0, '#sk3'('#sk1'))
86.84/87.45	              |  g_false_only('#sk3'('#sk1'), X0)
86.84/87.45	              | ~ g_both('#sk3'('#sk1'), X0)))),
86.84/87.45	    inference('split', [status(esa)], ['513'])).
86.84/87.45	tff('515', plain,
86.84/87.45	    (( g_false_only('#sk1', '#sk3'('#sk1'))
86.84/87.45	      |  g_false_only('#sk3'('#sk1'), '#sk1')))
86.84/87.45	      <= ((![X0]:
86.84/87.45	             ( g_false_only(X0, '#sk3'('#sk1'))
86.84/87.45	              |  g_false_only('#sk3'('#sk1'), X0)
86.84/87.45	              | ~ g_both('#sk3'('#sk1'), X0)))),
86.84/87.45	    inference('s_sup-', [status(thm)], ['510', '514'])).
86.84/87.45	tff('516', plain,
86.84/87.45	    ( g_false_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.45	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.45	    ~
86.84/87.45	    (![X0]:
86.84/87.45	       ( g_false_only(X0, '#sk3'('#sk1'))
86.84/87.45	        |  g_false_only('#sk3'('#sk1'), X0)
86.84/87.45	        | ~ g_both('#sk3'('#sk1'), X0))),
86.84/87.45	    inference('split', [status(esa)], ['515'])).
86.84/87.45	tff('517', plain,  g_both('#sk3'('#sk1'), '#sk1'),
86.84/87.45	    inference('simpl_trail', [status(thm)], ['508', '509'])).
86.84/87.45	tff('518', plain,
86.84/87.45	    (![X1, X2, X3]:
86.84/87.45	       ( '#form5'(X1)
86.84/87.45	        |  g_false_only(X3, X2)
86.84/87.45	        |  g_false_only(X2, X3)
86.84/87.45	        |  g_true_only(X2, '#sk4'(X2))
86.84/87.45	        | ~ g_both(X2, X1)
86.84/87.45	        | ~ g_both(X2, X3)))
86.84/87.45	      <= (~
86.84/87.45	          ( (??((^[Y0 : $i]:
86.84/87.45	                   ((??((^[Y1 : $i]:
86.84/87.45	                           ((~((??((^[Y2 : $i]:
86.84/87.45	                                      (g_true_only(Y1, Y2) &
86.84/87.45	                                       g_true_only(Y2, Y1)))))))&
86.84/87.45	                            (??((^[Y2 : $i]:
86.84/87.45	                                   ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.45	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                    (~(g_false_only(Y1, Y2)))))))&
86.84/87.45	                            g_both(Y1, Y0))))) &
86.84/87.45	                    (~((??((^[Y1 : $i]:
86.84/87.45	                              ((((!!((^[Y2 : $i]:
86.84/87.45	                                        (g_false_only(Y1, Y2) |
86.84/87.45	                                         g_false_only(Y2, Y1))))) |
86.84/87.45	                                 (??((^[Y2 : $i]:
86.84/87.45	                                        (g_true_only(Y1, Y2) &
86.84/87.45	                                         g_true_only(Y2, Y1)))))) &
86.84/87.45	                                g_both(Y1, Y0))|
86.84/87.45	                               (g_false_only(Y1, Y0) &
86.84/87.45	                                (((??((^[Y2 : $i]:
86.84/87.45	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.45	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.45	                                  (~((??((^[Y2 : $i]:
86.84/87.45	                                            (g_true_only(Y2, Y1) &
86.84/87.45	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.45	                                 (!!((^[Y2 : $i]:
86.84/87.45	                                        (g_false_only(Y2, Y1) |
86.84/87.45	                                         g_false_only(Y1, Y2)))))))|
86.84/87.45	                               ((((??((^[Y2 : $i]:
86.84/87.45	                                         ((~(g_false_only(Y1, Y2)))&
86.84/87.45	                                          (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                          (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.45	                                  (~((??((^[Y2 : $i]:
86.84/87.45	                                            (g_true_only(Y2, Y1) &
86.84/87.45	                                             g_true_only(Y1, Y2)))))))) |
86.84/87.45	                                 (??((^[Y2 : $i]:
86.84/87.45	                                        (g_true_only(Y1, Y2) &
86.84/87.45	                                         g_true_only(Y2, Y1)))))) &
86.84/87.45	                                g_true_only(Y1, Y0)))))))))))))),
86.84/87.45	    inference('renaming', [status(thm)], ['84', '85'])).
86.84/87.45	tff('519', plain,
86.84/87.45	    ~
86.84/87.45	    ( (??((^[Y0 : $i]:
86.84/87.45	             ((??((^[Y1 : $i]:
86.84/87.45	                     ((~((??((^[Y2 : $i]:
86.84/87.45	                                (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))))&
86.84/87.45	                      (??((^[Y2 : $i]:
86.84/87.45	                             ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.45	                              (~(g_false_only(Y2, Y1)))&
86.84/87.45	                              (~(g_false_only(Y1, Y2)))))))&
86.84/87.45	                      g_both(Y1, Y0))))) &
86.84/87.45	              (~((??((^[Y1 : $i]:
86.84/87.45	                        ((((!!((^[Y2 : $i]:
86.84/87.45	                                  (g_false_only(Y1, Y2) |
86.84/87.45	                                   g_false_only(Y2, Y1))))) |
86.84/87.45	                           (??((^[Y2 : $i]:
86.84/87.45	                                  (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) &
86.84/87.45	                          g_both(Y1, Y0))|
86.84/87.45	                         (g_false_only(Y1, Y0) &
86.84/87.45	                          (((??((^[Y2 : $i]:
86.84/87.45	                                   ((~(g_false_only(Y1, Y2)))&
86.84/87.45	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                    (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.45	                            (~((??((^[Y2 : $i]:
86.84/87.45	                                      (g_true_only(Y2, Y1) &
86.84/87.45	                                       g_true_only(Y1, Y2)))))))) |
86.84/87.45	                           (!!((^[Y2 : $i]:
86.84/87.45	                                  (g_false_only(Y2, Y1) |
86.84/87.45	                                   g_false_only(Y1, Y2)))))))|
86.84/87.45	                         ((((??((^[Y2 : $i]:
86.84/87.45	                                   ((~(g_false_only(Y1, Y2)))&
86.84/87.45	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                    (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.45	                            (~((??((^[Y2 : $i]:
86.84/87.45	                                      (g_true_only(Y2, Y1) &
86.84/87.45	                                       g_true_only(Y1, Y2)))))))) |
86.84/87.45	                           (??((^[Y2 : $i]:
86.84/87.45	                                  (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) &
86.84/87.45	                          g_true_only(Y1, Y0))))))))))))),
86.84/87.45	    inference('sat_resolution*', [status(thm)],
86.84/87.45	              ['160', '164', '187', '193', '197', '201', '207', '213', 
86.84/87.45	               '214', '217', '223', '50', '57', '146', '178', '58'])).
86.84/87.45	tff('520', plain,
86.84/87.45	    ![X1, X2, X3]:
86.84/87.45	      ( '#form5'(X1)
86.84/87.45	       |  g_false_only(X3, X2)
86.84/87.45	       |  g_false_only(X2, X3)
86.84/87.45	       |  g_true_only(X2, '#sk4'(X2))
86.84/87.45	       | ~ g_both(X2, X1)
86.84/87.45	       | ~ g_both(X2, X3)),
86.84/87.45	    inference('simpl_trail', [status(thm)], ['518', '519'])).
86.84/87.45	tff('521', plain,
86.84/87.45	    ![X0]:
86.84/87.45	      ( '#form5'('#sk1')
86.84/87.45	       |  g_false_only(X0, '#sk3'('#sk1'))
86.84/87.45	       |  g_false_only('#sk3'('#sk1'), X0)
86.84/87.45	       |  g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))
86.84/87.45	       | ~ g_both('#sk3'('#sk1'), X0)),
86.84/87.45	    inference('s_sup-', [status(thm)], ['517', '520'])).
86.84/87.45	tff('522', plain,
86.84/87.45	    (![X0]:
86.84/87.45	       ( g_false_only(X0, '#sk3'('#sk1'))
86.84/87.45	        |  g_false_only('#sk3'('#sk1'), X0)
86.84/87.45	        | ~ g_both('#sk3'('#sk1'), X0))) | 
86.84/87.45	    ( '#form5'('#sk1')) | 
86.84/87.45	    ( g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))),
86.84/87.45	    inference('split', [status(esa)], ['521'])).
86.84/87.45	tff('523', plain,
86.84/87.45	    ( g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1'))))
86.84/87.45	      <= (( g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1'))))),
86.84/87.45	    inference('split', [status(esa)], ['143'])).
86.84/87.45	tff('524', plain,
86.84/87.45	    ( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1')))
86.84/87.45	      <= (( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1')))),
86.84/87.45	    inference('split', [status(esa)], ['244'])).
86.84/87.45	tff('525', plain,
86.84/87.45	    ( g_both('#sk3'('#sk1'), '#sk1')) <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.45	    inference('split', [status(esa)], ['61'])).
86.84/87.45	tff('526', plain,
86.84/87.45	    ![X1, X2]:
86.84/87.45	      (~ g_true_only(X2, X1) | ~ g_true_only(X1, X2) | ~ g_both(X1, '#sk1')),
86.84/87.45	    inference('lazy_cnf_and', [status(thm)], ['232'])).
86.84/87.45	tff('527', plain,
86.84/87.45	    (![X0]:
86.84/87.45	       (~ g_true_only(X0, '#sk3'('#sk1')) | ~ g_true_only('#sk3'('#sk1'), X0)))
86.84/87.45	      <= (( g_both('#sk3'('#sk1'), '#sk1'))),
86.84/87.45	    inference('s_sup-', [status(thm)], ['525', '526'])).
86.84/87.45	tff('528', plain,
86.84/87.45	    (~ g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1'))))
86.84/87.45	      <= (( g_both('#sk3'('#sk1'), '#sk1')) & 
86.84/87.45	          ( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1')))),
86.84/87.45	    inference('s_sup-', [status(thm)], ['524', '527'])).
86.84/87.45	tff('529', plain,
86.84/87.45	    ~ ( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1'))) | 
86.84/87.45	    ~ ( g_true_only('#sk3'('#sk1'), '#sk4'('#sk3'('#sk1')))) | 
86.84/87.45	    ~ ( g_both('#sk3'('#sk1'), '#sk1')),
86.84/87.45	    inference('s_sup-', [status(thm)], ['523', '528'])).
86.84/87.45	tff('530', plain,
86.84/87.45	    ( g_true_only('#sk4'('#sk3'('#sk1')), '#sk3'('#sk1'))) | 
86.84/87.45	    (![X0]: ( '#form5'(X0) | ~ g_both('#sk3'('#sk1'), X0))) | 
86.84/87.45	    ( g_false_only('#sk1', '#sk3'('#sk1'))) | 
86.84/87.45	    ( (??((^[Y0 : $i]:
86.84/87.45	             ((??((^[Y1 : $i]:
86.84/87.45	                     ((~((??((^[Y2 : $i]:
86.84/87.45	                                (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))))&
86.84/87.45	                      (??((^[Y2 : $i]:
86.84/87.45	                             ((g_both(Y1, Y2) | g_both(Y2, Y1))&
86.84/87.45	                              (~(g_false_only(Y2, Y1)))&
86.84/87.45	                              (~(g_false_only(Y1, Y2)))))))&
86.84/87.45	                      g_both(Y1, Y0))))) &
86.84/87.45	              (~((??((^[Y1 : $i]:
86.84/87.45	                        ((((!!((^[Y2 : $i]:
86.84/87.45	                                  (g_false_only(Y1, Y2) |
86.84/87.45	                                   g_false_only(Y2, Y1))))) |
86.84/87.45	                           (??((^[Y2 : $i]:
86.84/87.45	                                  (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) &
86.84/87.45	                          g_both(Y1, Y0))|
86.84/87.45	                         (g_false_only(Y1, Y0) &
86.84/87.45	                          (((??((^[Y2 : $i]:
86.84/87.45	                                   ((~(g_false_only(Y1, Y2)))&
86.84/87.45	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                    (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.45	                            (~((??((^[Y2 : $i]:
86.84/87.45	                                      (g_true_only(Y2, Y1) &
86.84/87.45	                                       g_true_only(Y1, Y2)))))))) |
86.84/87.45	                           (!!((^[Y2 : $i]:
86.84/87.45	                                  (g_false_only(Y2, Y1) |
86.84/87.45	                                   g_false_only(Y1, Y2)))))))|
86.84/87.45	                         ((((??((^[Y2 : $i]:
86.84/87.45	                                   ((~(g_false_only(Y1, Y2)))&
86.84/87.45	                                    (~(g_false_only(Y2, Y1)))&
86.84/87.45	                                    (g_both(Y2, Y1) | g_both(Y1, Y2)))))) &
86.84/87.45	                            (~((??((^[Y2 : $i]:
86.84/87.45	                                      (g_true_only(Y2, Y1) &
86.84/87.45	                                       g_true_only(Y1, Y2)))))))) |
86.84/87.45	                           (??((^[Y2 : $i]:
86.84/87.45	                                  (g_true_only(Y1, Y2) & g_true_only(Y2, Y1)))))) &
86.84/87.45	                          g_true_only(Y1, Y0))))))))))))) | 
86.84/87.45	    ( g_false_only('#sk3'('#sk1'), '#sk1')) | 
86.84/87.45	    ~ ( g_both('#sk3'('#sk1'), '#sk1')),
86.84/87.45	    inference('split', [status(esa)], ['77'])).
86.84/87.45	tff('531', plain, $false,
86.84/87.45	    inference('sat_resolution*', [status(thm)],
86.84/87.45	              ['50', '57', '58', '251', '252', '140', '253', '236', '254', 
86.84/87.45	               '249', '262', '266', '280', '284', '288', '296', '303', 
86.84/87.45	               '317', '318', '322', '326', '330', '331', '346', '354', 
86.84/87.45	               '374', '387', '394', '409', '416', '417', '418', '429', 
86.84/87.45	               '434', '443', '450', '455', '461', '464', '465', '469', 
86.84/87.45	               '473', '477', '481', '488', '489', '497', '146', '237', 
86.84/87.45	               '238', '498', '187', '499', '240', '241', '207', '213', 
86.84/87.45	               '214', '217', '223', '152', '516', '522', '529', '530'])).
86.84/87.45	
86.84/87.45	% SZS output end Refutation
86.84/87.45	
86.84/87.45	% Zipperpin 1.5 exiting
86.84/87.45	EOF