0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rE0bKZUTb8 true
0.14/0.34	% Computer   : n020.cluster.edu
0.14/0.34	% Model      : x86_64 x86_64
0.14/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.34	% Memory     : 8042.1875MB
0.14/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.34	% CPULimit   : 1200
0.14/0.34	% WCLimit    : 120
0.14/0.34	% DateTime   : Tue Jul 13 13:05:36 EDT 2021
0.14/0.34	% CPUTime    : 
0.14/0.34	% Running portfolio for 120 s
0.14/0.34	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.14/0.34	% Number of cores: 8
0.14/0.34	% Python version: Python 3.6.8
0.14/0.35	% Running in HO mode
0.56/0.64	% Total configuration time : 828
0.56/0.64	% Estimated wc time : 983
0.56/0.64	% Estimated cpu time (8 cpus) : 122.875
0.56/0.69	% /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s
0.56/0.73	% /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s
0.56/0.73	% /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s
0.56/0.73	% /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s
0.56/0.74	% /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s
0.56/0.74	% /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s
0.56/0.75	% /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s
0.57/0.77	% /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s
0.57/0.77	% /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s
67.86/9.38	% Solved by lams/30_b.l.sh.
67.86/9.38	% running E: timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.rE0bKZUTb8/e_inputbf7575 --cpu-limit=12 --auto -s -p
67.86/9.38	% done 127 iterations in 8.525s
67.86/9.38	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
67.86/9.38	% SZS output start Refutation
67.86/9.38	thf('#sk24_type', type, '#sk24': $i > $i > $i > $o).
67.86/9.38	thf('#form84_type', type, '#form84': ($i > $i > $o) > $o).
67.86/9.38	thf('#form215_type', type, '#form215': $i > $i > $o).
67.86/9.38	thf('#sk3_type', type, '#sk3': $i).
67.86/9.38	thf(trc_type, type, trc: ($i > $i > $o) > $i > $i > $o).
67.86/9.38	thf(trans_type, type, trans: ($i > $i > $o) > $o).
67.86/9.38	thf('#sk2_type', type, '#sk2': $i).
67.86/9.38	thf(tc_type, type, tc: ($i > $i > $o) > $i > $i > $o).
67.86/9.38	thf('#sk4_type', type, '#sk4': $i).
67.86/9.38	thf('#sk23_type', type, '#sk23': $i > $i > $i > $o).
67.86/9.38	thf('#sk1_type', type, '#sk1': $i > $i > $o).
67.86/9.38	thf(lconfl_type, type, lconfl: ($i > $i > $o) > $o).
67.86/9.38	thf('#form6_type', type, '#form6': $i > $o).
67.86/9.38	thf(rc_type, type, rc: ($i > $i > $o) > $i > $i > $o).
67.86/9.38	thf('#sk5_type', type, '#sk5': $i > $i > $i).
67.86/9.38	thf(subrel_type, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
67.86/9.38	thf('#sk85_type', type, '#sk85': ($i > $i > $o) > $i).
67.86/9.38	thf(join_type, type, join: ($i > $i > $o) > $i > $i > $o).
67.86/9.38	thf('#sk49_type', type, '#sk49': ($i > $i > $o) > $i).
67.86/9.38	thf('#sk98_type', type, '#sk98': ($i > $i > $o) > $i).
67.86/9.38	thf('#sk244_type', type, '#sk244': $i > $i > $i > $i > $o).
67.86/9.38	thf('#sk118_type', type, '#sk118': ($i > $i > $o) > $i).
67.86/9.38	thf(confl_type, type, confl: ($i > $i > $o) > $o).
67.86/9.38	thf('#form68_type', type, '#form68': ($i > $i > $o) > $o).
67.86/9.38	thf('#sk69_type', type, '#sk69': ($i > $i > $o) > $i).
67.86/9.38	thf(confluence_implies_local_confluence, conjecture,
67.86/9.38	  (![R:( $i > $i > $o )]: ( ( confl @ R ) => ( lconfl @ R ) ))).
67.86/9.38	thf(zf_stmt_0, negated_conjecture,
67.86/9.38	  (~( ![R:( $i > $i > $o )]: ( ( confl @ R ) => ( lconfl @ R ) ) )),
67.86/9.38	  inference('cnf.neg', [status(esa)], [confluence_implies_local_confluence])).
67.86/9.38	thf(zip_derived_cl0, plain,
67.86/9.38	    (~ (((!!) @ (^[Y0 : $i > $i > $o]: (((confl @ Y0) => (lconfl @ Y0))))))),
67.86/9.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
67.86/9.38	thf(zip_derived_cl1, plain, (~ (((confl @ '#sk1') => (lconfl @ '#sk1')))),
67.86/9.38	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])).
67.86/9.38	thf(zip_derived_cl3, plain, (~ (lconfl @ '#sk1')),
67.86/9.38	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])).
67.86/9.38	thf(locally_confluent, axiom, ~ (lconfl @ X0) =>
67.86/9.38	  ((((!!) @ (^[Y0 : $i]:
67.86/9.38	               (((!!) @ (^[Y1 : $i]:
67.86/9.38	                           (((!!) @ (^[Y2 : $i]:
67.86/9.38	                                       (((((X0 @ Y0 @ Y1) & (X0 @ Y0 @ Y2))) =>
67.86/9.38	                                         (join @ X0 @ Y2 @ Y1))))))))))))
67.86/9.38	   != ($true))).
67.86/9.38	thf('0', plain,
67.86/9.38	    (![X0:( $i > $i > $o )]:
67.86/9.38	     ( ( ~( lconfl @ X0 ) ) <=>
67.86/9.38	       ( ~( ![X5:$i,X7:$i,X9:$i]:
67.86/9.38	            ( ( ( X0 @ X5 @ X7 ) & ( X0 @ X5 @ X9 ) ) =>
67.86/9.38	              ( join @ X0 @ X9 @ X7 ) ) ) ) )),
67.86/9.38	    inference('rw.lit', [status(esa)], [locally_confluent])).
67.86/9.38	thf(zip_derived_cl5, plain,
67.86/9.38	    (~ (((!!) @ (^[Y0 : $i]:
67.86/9.38	                   (((!!) @ (^[Y1 : $i]:
67.86/9.38	                               (((!!) @ (^[Y2 : $i]:
67.86/9.38	                                           ((((('#sk1' @ Y0 @ Y1) &
67.86/9.38	                                               ('#sk1' @ Y0 @ Y2))) =>
67.86/9.38	                                             (join @ '#sk1' @ Y2 @ Y1))))))))))))),
67.86/9.38	    inference('rw_clause', [status(thm)], [zip_derived_cl3, '0'])).
67.86/9.38	thf(zip_derived_cl7, plain,
67.86/9.38	    (~ (((!!) @ (^[Y0 : $i]:
67.86/9.38	                   (((!!) @ (^[Y1 : $i]:
67.86/9.38	                               ((((('#sk1' @ '#sk2' @ Y0) & ('#sk1' @ 
67.86/9.38	                                   '#sk2' @ Y1))) =>
67.86/9.38	                                 (join @ '#sk1' @ Y1 @ Y0)))))))))),
67.86/9.38	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])).
67.86/9.38	thf(zip_derived_cl9, plain,
67.86/9.38	    (~ (((!!) @ (^[Y0 : $i]:
67.86/9.38	                   ((((('#sk1' @ '#sk2' @ '#sk3') & ('#sk1' @ '#sk2' @ Y0))) =>
67.86/9.38	                     (join @ '#sk1' @ Y0 @ '#sk3'))))))),
67.86/9.38	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])).
67.86/9.38	thf(zip_derived_cl12, plain,
67.86/9.38	    (~ ((((('#sk1' @ '#sk2' @ '#sk3') & ('#sk1' @ '#sk2' @ '#sk4'))) =>
67.86/9.38	         (join @ '#sk1' @ '#sk4' @ '#sk3')))),
67.86/9.38	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])).
67.86/9.38	thf(zip_derived_cl16, plain, (~ (join @ '#sk1' @ '#sk4' @ '#sk3')),
67.86/9.38	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])).
67.86/9.38	thf(joinable, axiom, ~ (join @ X0 @ X1 @ X2) =>
67.86/9.38	  ((((??) @ (^[Y0 : $i]: (((trc @ X0 @ X1 @ Y0) & (trc @ X0 @ X2 @ Y0))))))
67.86/9.38	   != ($true))).
67.86/9.38	thf('1', plain,
67.86/9.38	    (![X0:( $i > $i > $o ),X1:$i,X2:$i]:
67.86/9.38	     ( ( ~( join @ X0 @ X1 @ X2 ) ) <=>
67.86/9.38	       ( ~( ?[X7:$i]: ( ( trc @ X0 @ X1 @ X7 ) & ( trc @ X0 @ X2 @ X7 ) ) ) ) )),
67.86/9.38	    inference('rw.lit', [status(esa)], [joinable])).
67.86/9.38	thf(zip_derived_cl20, plain,
67.86/9.38	    (~ (((??) @ (^[Y0 : $i]:
67.86/9.38	                   (((trc @ '#sk1' @ '#sk4' @ Y0) & (trc @ '#sk1' @ '#sk3' @ 
67.86/9.38	                     Y0))))))),
67.86/9.38	    inference('rw_clause', [status(thm)], [zip_derived_cl16, '1'])).
67.86/9.38	thf(zip_derived_cl22, plain,
67.86/9.38	    (![X2 : $i]:
67.86/9.38	       ~ (((trc @ '#sk1' @ '#sk4' @ X2) & (trc @ '#sk1' @ '#sk3' @ X2)))),
67.86/9.38	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])).
67.86/9.38	thf(transitive_reflexive_closure, axiom,(( trc @ (X0)@ (X1)@ (X2)) =
67.86/9.38	  ((rc @ (tc @ X0) @ X1 @ X2)))).
67.86/9.38	thf('2', plain,
67.86/9.38	    (![X2:$i,X1:$i,X0:( $i > $i > $o )]:
67.86/9.38	     ( ( trc @ X0 @ X1 @ X2 ) = ( rc @ ( tc @ X0 ) @ X1 @ X2 ) )),
67.86/9.38	    define([status(thm)])).
67.86/9.38	thf(zip_derived_cl26, plain,
67.86/9.38	    (![X2 : $i]:
67.86/9.38	       ~ (((rc @ (tc @ '#sk1') @ '#sk4' @ X2) & (rc @ (tc @ '#sk1') @ 
67.86/9.38	           '#sk3' @ X2)))),
67.86/9.38	    inference('rw', [status(thm)], [zip_derived_cl22, '2', '2'])).
67.86/9.38	thf(zip_derived_cl27, plain,
67.86/9.38	    (![X2 : $i]:
67.86/9.38	       (~ (rc @ (tc @ '#sk1') @ '#sk4' @ X2)
67.86/9.38	        | ~ (rc @ (tc @ '#sk1') @ '#sk3' @ X2))),
67.86/9.38	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])).
67.86/9.38	thf(reflexive_closure, axiom, ~ (rc @ X0 @ X1 @ X2) =>
67.86/9.38	  ((((X0 @ X1 @ X2) | (((X1) = (X2))))) != ($true))).
67.86/9.38	thf('3', plain,
67.86/9.38	    (![X0:( $i > $i > $o ),X1:$i,X2:$i]:
67.86/9.38	     ( ( ~( rc @ X0 @ X1 @ X2 ) ) <=>
67.86/9.38	       ( ~( ( X0 @ X1 @ X2 ) | ( ( X1 ) = ( X2 ) ) ) ) )),
67.86/9.38	    inference('rw.lit', [status(esa)], [reflexive_closure])).
67.86/9.38	thf(zip_derived_cl30, plain,
67.86/9.38	    (![X0 : $i]:
67.86/9.38	       (~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0)))))
67.86/9.38	        | ~ (rc @ (tc @ '#sk1') @ '#sk3' @ X0))),
67.86/9.38	    inference('rw_clause', [status(thm)], [zip_derived_cl27, '3'])).
67.86/9.38	thf(zip_derived_cl33, plain,
67.86/9.38	    (![X0 : $i]:
67.86/9.38	       (~ (((tc @ '#sk1' @ '#sk3' @ X0) | ((('#sk3') = (X0)))))
67.86/9.38	        | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))),
67.86/9.38	    inference('rw_clause', [status(thm)], [zip_derived_cl30, '3'])).
67.86/9.38	thf(zip_derived_cl39, plain,
67.86/9.38	    (![X0 : $i]:
67.86/9.38	       (~ ((('#sk3') = (X0)))
67.86/9.38	        | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))),
67.86/9.38	    inference('lazy_cnf_or', [status(thm)], [zip_derived_cl33])).
67.86/9.38	thf(zip_derived_cl46, plain,
67.86/9.38	    (![X0 : $i]:
67.86/9.38	       ((('#sk3') != (X0))
67.86/9.38	        | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))),
67.86/9.38	    inference('simplify nested equalities', [status(thm)], [zip_derived_cl39])).
67.86/9.38	thf(zip_derived_cl47, plain,
67.86/9.38	    (~ (((tc @ '#sk1' @ '#sk4' @ '#sk3') | ((('#sk4') = ('#sk3')))))),
67.86/9.38	    inference('simplify', [status(thm)], [zip_derived_cl46])).
67.86/9.38	thf(zip_derived_cl38, plain,
67.86/9.38	    (![X0 : $i]:
67.86/9.38	       (~ (tc @ '#sk1' @ '#sk3' @ X0)
67.86/9.38	        | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))),
67.86/9.38	    inference('lazy_cnf_or', [status(thm)], [zip_derived_cl33])).
67.86/9.38	thf(zip_derived_cl42, plain,
67.86/9.38	    (![X0 : $i]:
67.86/9.38	       ( ('#form6' @ X0)
67.86/9.38	        | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))),
67.86/9.38	    define([status(thm)])).
67.86/9.38	thf(zip_derived_cl48, plain, (~ ('#form6' @ '#sk3')),
67.86/9.38	    inference('renaming', [status(thm)], [zip_derived_cl47, zip_derived_cl42])).
67.86/9.38	thf(zip_derived_cl42, plain,
67.86/9.38	    (![X0 : $i]:
67.86/9.38	       ( ('#form6' @ X0)
67.86/9.38	        | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))),
67.86/9.38	    define([status(thm)])).
67.86/9.38	thf(zip_derived_cl44, plain,
67.86/9.38	    (![X0 : $i]: (~ ((('#sk4') = (X0))) |  ('#form6' @ X0))),
67.86/9.38	    inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])).
67.86/9.38	thf(zip_derived_cl53, plain,
67.86/9.38	    (![X0 : $i]: ((('#sk4') != (X0)) |  ('#form6' @ X0))),
67.86/9.39	    inference('simplify nested equalities', [status(thm)], [zip_derived_cl44])).
67.86/9.39	thf(zip_derived_cl54, plain, ( ('#form6' @ '#sk4')),
67.86/9.39	    inference('simplify', [status(thm)], [zip_derived_cl53])).
67.86/9.39	thf(zip_derived_cl2, plain, ( (confl @ '#sk1')),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])).
67.86/9.39	thf(confluent, axiom, (confl @ X0) =>
67.86/9.39	  ((((!!) @ (^[Y0 : $i]:
67.86/9.39	               (((!!) @ (^[Y1 : $i]:
67.86/9.39	                           (((!!) @ (^[Y2 : $i]:
67.86/9.39	                                       (((((trc @ X0 @ Y0 @ Y1) & (trc @ 
67.86/9.39	                                           X0 @ Y0 @ Y2))) =>
67.86/9.39	                                         (join @ X0 @ Y2 @ Y1))))))))))))
67.86/9.39	   = ($true))).
67.86/9.39	thf('4', plain,
67.86/9.39	    (![X0:( $i > $i > $o )]:
67.86/9.39	     ( ( confl @ X0 ) <=>
67.86/9.39	       ( ![X5:$i,X7:$i,X9:$i]:
67.86/9.39	         ( ( ( trc @ X0 @ X5 @ X7 ) & ( trc @ X0 @ X5 @ X9 ) ) =>
67.86/9.39	           ( join @ X0 @ X9 @ X7 ) ) ) )),
67.86/9.39	    inference('rw.lit', [status(esa)], [confluent])).
67.86/9.39	thf(zip_derived_cl4, plain,
67.86/9.39	    ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                  (((!!) @ (^[Y1 : $i]:
67.86/9.39	                              (((!!) @ (^[Y2 : $i]:
67.86/9.39	                                          (((((trc @ '#sk1' @ Y0 @ Y1) &
67.86/9.39	                                              (trc @ '#sk1' @ Y0 @ Y2))) =>
67.86/9.39	                                            (join @ '#sk1' @ Y2 @ Y1))))))))))))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl2, '4'])).
67.86/9.39	thf(zip_derived_cl6, plain,
67.86/9.39	    (![X2 : $i]:
67.86/9.39	        (((!!) @ (^[Y0 : $i]:
67.86/9.39	                    (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                (((((trc @ '#sk1' @ X2 @ Y0) & (trc @ 
67.86/9.39	                                    '#sk1' @ X2 @ Y1))) =>
67.86/9.39	                                  (join @ '#sk1' @ Y1 @ Y0)))))))))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])).
67.86/9.39	thf(zip_derived_cl8, plain,
67.86/9.39	    (![X2 : $i, X4 : $i]:
67.86/9.39	        (((!!) @ (^[Y0 : $i]:
67.86/9.39	                    (((((trc @ '#sk1' @ X2 @ X4) & (trc @ '#sk1' @ X2 @ Y0))) =>
67.86/9.39	                      (join @ '#sk1' @ Y0 @ X4))))))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])).
67.86/9.39	thf(zip_derived_cl10, plain,
67.86/9.39	    (![X2 : $i, X4 : $i]:
67.86/9.39	        (((!!) @ (^[Y0 : $i]:
67.86/9.39	                    (((((rc @ (tc @ '#sk1') @ X2 @ X4) & (trc @ '#sk1' @ 
67.86/9.39	                        X2 @ Y0))) =>
67.86/9.39	                      (join @ '#sk1' @ Y0 @ X4))))))),
67.86/9.39	    inference('rw', [status(thm)], [zip_derived_cl8, '2'])).
67.86/9.39	thf(zip_derived_cl11, plain,
67.86/9.39	    (![X2 : $i, X4 : $i, X6 : $i]:
67.86/9.39	        (((((rc @ (tc @ '#sk1') @ X2 @ X4) & (trc @ '#sk1' @ X2 @ X6))) =>
67.86/9.39	          (join @ '#sk1' @ X6 @ X4)))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])).
67.86/9.39	thf(zip_derived_cl13, plain,
67.86/9.39	    (![X2 : $i, X4 : $i, X6 : $i]:
67.86/9.39	        (((((rc @ (tc @ '#sk1') @ X2 @ X4) & (rc @ (tc @ '#sk1') @ X2 @ X6))) =>
67.86/9.39	          (join @ '#sk1' @ X6 @ X4)))),
67.86/9.39	    inference('rw', [status(thm)], [zip_derived_cl11, '2'])).
67.86/9.39	thf(zip_derived_cl14, plain,
67.86/9.39	    (![X2 : $i, X4 : $i, X6 : $i]:
67.86/9.39	       (~ (((rc @ (tc @ '#sk1') @ X2 @ X4) & (rc @ (tc @ '#sk1') @ X2 @ X6)))
67.86/9.39	        |  (join @ '#sk1' @ X6 @ X4))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
67.86/9.39	thf(joinable, axiom, (join @ X0 @ X1 @ X2) =>
67.86/9.39	  ((((??) @ (^[Y0 : $i]: (((trc @ X0 @ X1 @ Y0) & (trc @ X0 @ X2 @ Y0)))))) =
67.86/9.39	   ($true))).
67.86/9.39	thf('5', plain,
67.86/9.39	    (![X0:( $i > $i > $o ),X1:$i,X2:$i]:
67.86/9.39	     ( ( join @ X0 @ X1 @ X2 ) <=>
67.86/9.39	       ( ?[X7:$i]: ( ( trc @ X0 @ X1 @ X7 ) & ( trc @ X0 @ X2 @ X7 ) ) ) )),
67.86/9.39	    inference('rw.lit', [status(esa)], [joinable])).
67.86/9.39	thf(zip_derived_cl17, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (((??) @ (^[Y0 : $i]:
67.86/9.39	                     (((trc @ '#sk1' @ X0 @ Y0) & (trc @ '#sk1' @ X2 @ Y0))))))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl14, '5'])).
67.86/9.39	thf(zip_derived_cl21, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (((trc @ '#sk1' @ X0 @ ('#sk5' @ X0 @ X2)) & (trc @ '#sk1' @ X2 @ 
67.86/9.39	           ('#sk5' @ X0 @ X2))))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl17])).
67.86/9.39	thf(zip_derived_cl23, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (((rc @ (tc @ '#sk1') @ X0 @ ('#sk5' @ X0 @ X2)) & (rc @ 
67.86/9.39	           (tc @ '#sk1') @ X2 @ ('#sk5' @ X0 @ X2))))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('rw', [status(thm)], [zip_derived_cl21, '2', '2'])).
67.86/9.39	thf(zip_derived_cl24, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (rc @ (tc @ '#sk1') @ X0 @ ('#sk5' @ X0 @ X2))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])).
67.86/9.39	thf(reflexive_closure, axiom, (rc @ X0 @ X1 @ X2) =>
67.86/9.39	  ((((X0 @ X1 @ X2) | (((X1) = (X2))))) = ($true))).
67.86/9.39	thf('6', plain,
67.86/9.39	    (![X0:( $i > $i > $o ),X1:$i,X2:$i]:
67.86/9.39	     ( ( rc @ X0 @ X1 @ X2 ) <=> ( ( ( X1 ) = ( X2 ) ) | ( X0 @ X1 @ X2 ) ) )),
67.86/9.39	    inference('rw.lit', [status(esa)], [reflexive_closure])).
67.86/9.39	thf(zip_derived_cl28, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (((tc @ '#sk1' @ X0 @ ('#sk5' @ X0 @ X2)) |
67.86/9.39	           (((X0) = ('#sk5' @ X0 @ X2)))))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl24, '6'])).
67.86/9.39	thf(zip_derived_cl31, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (tc @ '#sk1' @ X0 @ ('#sk5' @ X0 @ X2))
67.86/9.39	        |  (((X0) = ('#sk5' @ X0 @ X2)))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('lazy_cnf_or', [status(thm)], [zip_derived_cl28])).
67.86/9.39	thf(zip_derived_cl34, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (tc @ '#sk1' @ X0 @ ('#sk5' @ X0 @ X2))
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X2))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('simplify nested equalities', [status(thm)], [zip_derived_cl31])).
67.86/9.39	thf(transitive_closure, axiom, (tc @ X0 @ X1 @ X2) =>
67.86/9.39	  ((((!!) @ (^[Y0 : $i > $i > $o]:
67.86/9.39	               (((((subrel @ X0 @ Y0) & (trans @ Y0))) => (Y0 @ X1 @ X2))))))
67.86/9.39	   = ($true))).
67.86/9.39	thf('7', plain,
67.86/9.39	    (![X0:( $i > $i > $o ),X1:$i,X2:$i]:
67.86/9.39	     ( ( tc @ X0 @ X1 @ X2 ) <=>
67.86/9.39	       ( ![X7:( $i > $i > $o )]:
67.86/9.39	         ( ( ( subrel @ X0 @ X7 ) & ( trans @ X7 ) ) => ( X7 @ X1 @ X2 ) ) ) )),
67.86/9.39	    inference('rw.lit', [status(esa)], [transitive_closure])).
67.86/9.39	thf(zip_derived_cl35, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i > $i > $o]:
67.86/9.39	                     (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 
67.86/9.39	                       X0 @ ('#sk5' @ X0 @ X2)))))))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0)))
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X2)))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl34, '7'])).
67.86/9.39	thf(zip_derived_cl40, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]:
67.86/9.39	       ( (((((subrel @ '#sk1' @ X4) & (trans @ X4))) => (X4 @ X0 @ 
67.86/9.39	           ('#sk5' @ X0 @ X2))))
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X2))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl35])).
67.86/9.39	thf(zip_derived_cl49, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]:
67.86/9.39	       (~ (((subrel @ '#sk1' @ X4) & (trans @ X4)))
67.86/9.39	        |  (X4 @ X0 @ ('#sk5' @ X0 @ X2))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0)))
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X2)))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
67.86/9.39	thf(zip_derived_cl55, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]:
67.86/9.39	       (~ (subrel @ '#sk1' @ X4)
67.86/9.39	        | ~ (trans @ X4)
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X2))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0)))
67.86/9.39	        |  (X4 @ X0 @ ('#sk5' @ X0 @ X2)))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl49])).
67.86/9.39	thf(subrel, axiom, ~ (subrel @ X0 @ X1) =>
67.86/9.39	  ((((!!) @ (^[Y0 : $i]:
67.86/9.39	               (((!!) @ (^[Y1 : $i]: (((X0 @ Y0 @ Y1) => (X1 @ Y0 @ Y1)))))))))
67.86/9.39	   != ($true))).
67.86/9.39	thf('8', plain,
67.86/9.39	    (![X0:( $i > $i > $o ),X1:( $i > $i > $o )]:
67.86/9.39	     ( ( ~( subrel @ X0 @ X1 ) ) <=>
67.86/9.39	       ( ~( ![X6:$i,X8:$i]: ( ( X0 @ X6 @ X8 ) => ( X1 @ X6 @ X8 ) ) ) ) )),
67.86/9.39	    inference('rw.lit', [status(esa)], [subrel])).
67.86/9.39	thf(zip_derived_cl59, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                      (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                  ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1)))))))))
67.86/9.39	        |  (X0 @ X2 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X3 @ X1) & (rc @ (tc @ '#sk1') @ X3 @ X2)))
67.86/9.39	        | ((X2) = ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ (trans @ X0))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl55, '8'])).
67.86/9.39	thf(transitive, axiom, ~ (trans @ X0) =>
67.86/9.39	  ((((!!) @ (^[Y0 : $i]:
67.86/9.39	               (((!!) @ (^[Y1 : $i]:
67.86/9.39	                           (((!!) @ (^[Y2 : $i]:
67.86/9.39	                                       (((((X0 @ Y1 @ Y2) & (X0 @ Y0 @ Y1))) =>
67.86/9.39	                                         (X0 @ Y0 @ Y2))))))))))))
67.86/9.39	   != ($true))).
67.86/9.39	thf('9', plain,
67.86/9.39	    (![X0:( $i > $i > $o )]:
67.86/9.39	     ( ( ~( trans @ X0 ) ) <=>
67.86/9.39	       ( ~( ![X5:$i,X7:$i,X9:$i]:
67.86/9.39	            ( ( ( X0 @ X7 @ X9 ) & ( X0 @ X5 @ X7 ) ) => ( X0 @ X5 @ X9 ) ) ) ) )),
67.86/9.39	    inference('rw.lit', [status(esa)], [transitive])).
67.86/9.39	thf(zip_derived_cl65, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                      (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                  (((!!) @ (^[Y2 : $i]:
67.86/9.39	                                              (((((X3 @ Y1 @ Y2) & (X3 @ 
67.86/9.39	                                                  Y0 @ Y1))) =>
67.86/9.39	                                                (X3 @ Y0 @ Y2))))))))))))
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0)))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl59, '9'])).
67.86/9.39	thf(zip_derived_cl71, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                      (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                  (((((X3 @ Y0 @ Y1) & (X3 @ 
67.86/9.39	                                      ('#sk49' @ X3) @ Y0))) =>
67.86/9.39	                                    (X3 @ ('#sk49' @ X3) @ Y1)))))))))
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1)))))))))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0)))
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X1)))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl65])).
67.86/9.39	thf(zip_derived_cl71, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                      (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                  (((((X3 @ Y0 @ Y1) & (X3 @ 
67.86/9.39	                                      ('#sk49' @ X3) @ Y0))) =>
67.86/9.39	                                    (X3 @ ('#sk49' @ X3) @ Y1)))))))))
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1)))))))))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0)))
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X1)))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl65])).
67.86/9.39	thf(zip_derived_cl77, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( ('#form68' @ X3)
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    (((((X3 @ Y0 @ Y1) & (X3 @ 
67.86/9.39	                                        ('#sk49' @ X3) @ Y0))) =>
67.86/9.39	                                      (X3 @ ('#sk49' @ X3) @ Y1))))))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl79, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ ('#form68' @ X3)
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0)))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    inference('renaming', [status(thm)], [zip_derived_cl71, zip_derived_cl77])).
67.86/9.39	thf(zip_derived_cl79, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ ('#form68' @ X3)
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0)))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    inference('renaming', [status(thm)], [zip_derived_cl71, zip_derived_cl77])).
67.86/9.39	thf(zip_derived_cl85, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( ('#form84' @ X3)
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl87, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ ('#form84' @ X3)
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0)))
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ ('#form68' @ X3))),
67.86/9.39	    inference('renaming', [status(thm)], [zip_derived_cl79, zip_derived_cl85])).
67.86/9.39	thf(zip_derived_cl95, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ (rc @ (tc @ '#sk1') @ X2 @ X1)
67.86/9.39	        | ~ (rc @ (tc @ '#sk1') @ X2 @ X0)
67.86/9.39	        | ~ ('#form68' @ X3)
67.86/9.39	        | ((X0) = ('#sk5' @ X0 @ X1))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X0 @ X1))
67.86/9.39	        | ~ ('#form84' @ X3))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl87])).
67.86/9.39	thf(zip_derived_cl105, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1)))))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        |  (X0 @ X2 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ((X2) = ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ~ (rc @ (tc @ '#sk1') @ X3 @ X2))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl95, '3'])).
67.86/9.39	thf(zip_derived_cl113, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1)))))
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ((X1) = ('#sk5' @ X1 @ X2))
67.86/9.39	        |  (X0 @ X1 @ ('#sk5' @ X1 @ X2))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl105, '3'])).
67.86/9.39	thf(zip_derived_cl117, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ (tc @ '#sk1' @ X3 @ X1)
67.86/9.39	        | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2)))))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        |  (X0 @ X1 @ ('#sk5' @ X1 @ X2))
67.86/9.39	        | ((X1) = ('#sk5' @ X1 @ X2))
67.86/9.39	        | ~ ('#form68' @ X0))),
67.86/9.39	    inference('lazy_cnf_or', [status(thm)], [zip_derived_cl113])).
67.86/9.39	thf(zip_derived_cl25, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (rc @ (tc @ '#sk1') @ X2 @ ('#sk5' @ X0 @ X2))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])).
67.86/9.39	thf(zip_derived_cl29, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (((tc @ '#sk1' @ X2 @ ('#sk5' @ X0 @ X2)) |
67.86/9.39	           (((X2) = ('#sk5' @ X0 @ X2)))))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl25, '6'])).
67.86/9.39	thf(zip_derived_cl32, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (tc @ '#sk1' @ X2 @ ('#sk5' @ X0 @ X2))
67.86/9.39	        |  (((X2) = ('#sk5' @ X0 @ X2)))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])).
67.86/9.39	thf(zip_derived_cl36, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (tc @ '#sk1' @ X2 @ ('#sk5' @ X0 @ X2))
67.86/9.39	        | ((X2) = ('#sk5' @ X0 @ X2))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('simplify nested equalities', [status(thm)], [zip_derived_cl32])).
67.86/9.39	thf(zip_derived_cl37, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i > $i > $o]:
67.86/9.39	                     (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 
67.86/9.39	                       X2 @ ('#sk5' @ X0 @ X2)))))))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0)))
67.86/9.39	        | ((X2) = ('#sk5' @ X0 @ X2)))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl36, '7'])).
67.86/9.39	thf(zip_derived_cl41, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]:
67.86/9.39	       ( (((((subrel @ '#sk1' @ X4) & (trans @ X4))) => (X4 @ X2 @ 
67.86/9.39	           ('#sk5' @ X0 @ X2))))
67.86/9.39	        | ((X2) = ('#sk5' @ X0 @ X2))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])).
67.86/9.39	thf(zip_derived_cl50, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]:
67.86/9.39	       (~ (((subrel @ '#sk1' @ X4) & (trans @ X4)))
67.86/9.39	        |  (X4 @ X2 @ ('#sk5' @ X0 @ X2))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0)))
67.86/9.39	        | ((X2) = ('#sk5' @ X0 @ X2)))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])).
67.86/9.39	thf(zip_derived_cl56, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]:
67.86/9.39	       (~ (subrel @ '#sk1' @ X4)
67.86/9.39	        | ~ (trans @ X4)
67.86/9.39	        | ((X2) = ('#sk5' @ X0 @ X2))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0)))
67.86/9.39	        |  (X4 @ X2 @ ('#sk5' @ X0 @ X2)))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl50])).
67.86/9.39	thf(zip_derived_cl60, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                      (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                  ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1)))))))))
67.86/9.39	        |  (X0 @ X1 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X3 @ X1) & (rc @ (tc @ '#sk1') @ X3 @ X2)))
67.86/9.39	        | ((X1) = ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ (trans @ X0))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl56, '8'])).
67.86/9.39	thf(zip_derived_cl66, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                      (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                  (((!!) @ (^[Y2 : $i]:
67.86/9.39	                                              (((((X3 @ Y1 @ Y2) & (X3 @ 
67.86/9.39	                                                  Y0 @ Y1))) =>
67.86/9.39	                                                (X3 @ Y0 @ Y2))))))))))))
67.86/9.39	        | ((X0) = ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1)))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl60, '9'])).
67.86/9.39	thf(zip_derived_cl72, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                      (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                  (((((X3 @ Y0 @ Y1) & (X3 @ 
67.86/9.39	                                      ('#sk49' @ X3) @ Y0))) =>
67.86/9.39	                                    (X3 @ ('#sk49' @ X3) @ Y1)))))))))
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1)))))))))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1)))
67.86/9.39	        | ((X0) = ('#sk5' @ X1 @ X0)))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl66])).
67.86/9.39	thf(zip_derived_cl77, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( ('#form68' @ X3)
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    (((((X3 @ Y0 @ Y1) & (X3 @ 
67.86/9.39	                                        ('#sk49' @ X3) @ Y0))) =>
67.86/9.39	                                      (X3 @ ('#sk49' @ X3) @ Y1))))))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl80, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ ('#form68' @ (^[Y0 : $i,Y1 : $i]: (X3 @ Y0 @ Y1)))
67.86/9.39	        | ((X0) = ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1)))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    inference('renaming', [status(thm)], [zip_derived_cl72, zip_derived_cl77])).
67.86/9.39	thf(zip_derived_cl89, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ ('#form68' @ X3)
67.86/9.39	        | ((X0) = ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1)))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    inference('ho_norm', [status(thm)], [zip_derived_cl80])).
67.86/9.39	thf(zip_derived_cl85, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( ('#form84' @ X3)
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl90, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ ('#form84' @ (^[Y0 : $i,Y1 : $i]: (X3 @ Y0 @ Y1)))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1)))
67.86/9.39	        | ((X0) = ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ ('#form68' @ X3))),
67.86/9.39	    inference('renaming', [status(thm)], [zip_derived_cl89, zip_derived_cl85])).
67.86/9.39	thf(zip_derived_cl99, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ ('#form84' @ X3)
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1)))
67.86/9.39	        | ((X0) = ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ ('#form68' @ X3))),
67.86/9.39	    inference('ho_norm', [status(thm)], [zip_derived_cl90])).
67.86/9.39	thf(zip_derived_cl100, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]:
67.86/9.39	       (~ (rc @ (tc @ '#sk1') @ X2 @ X0)
67.86/9.39	        | ~ (rc @ (tc @ '#sk1') @ X2 @ X1)
67.86/9.39	        | ~ ('#form68' @ X3)
67.86/9.39	        | ((X0) = ('#sk5' @ X1 @ X0))
67.86/9.39	        |  (X3 @ X0 @ ('#sk5' @ X1 @ X0))
67.86/9.39	        | ~ ('#form84' @ X3))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl99])).
67.86/9.39	thf(zip_derived_cl110, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1)))))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        |  (X0 @ X1 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ((X1) = ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ~ (rc @ (tc @ '#sk1') @ X3 @ X2))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl100, '3'])).
67.86/9.39	thf(zip_derived_cl114, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2)))))
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ((X1) = ('#sk5' @ X2 @ X1))
67.86/9.39	        |  (X0 @ X1 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        | ~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1))))))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl110, '3'])).
67.86/9.39	thf(zip_derived_cl119, plain,
67.86/9.39	    (![X2 : $i, X3 : $i]:
67.86/9.39	       ( ('#form215' @ X2 @ X3)
67.86/9.39	        | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl123, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ ('#form215' @ X2 @ X3)
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ((X1) = ('#sk5' @ X1 @ X2))
67.86/9.39	        |  (X0 @ X1 @ ('#sk5' @ X1 @ X2))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        | ~ (tc @ '#sk1' @ X3 @ X1))),
67.86/9.39	    inference('renaming', [status(thm)],
67.86/9.39	              [zip_derived_cl117, zip_derived_cl119])).
67.86/9.39	thf(transitive_closure, axiom, ~ (tc @ X0 @ X1 @ X2) =>
67.86/9.39	  ((((!!) @ (^[Y0 : $i > $i > $o]:
67.86/9.39	               (((((subrel @ X0 @ Y0) & (trans @ Y0))) => (Y0 @ X1 @ X2))))))
67.86/9.39	   != ($true))).
67.86/9.39	thf('10', plain,
67.86/9.39	    (![X0:( $i > $i > $o ),X1:$i,X2:$i]:
67.86/9.39	     ( ( ~( tc @ X0 @ X1 @ X2 ) ) <=>
67.86/9.39	       ( ~( ![X7:( $i > $i > $o )]:
67.86/9.39	            ( ( ( subrel @ X0 @ X7 ) & ( trans @ X7 ) ) => ( X7 @ X1 @ X2 ) ) ) ) )),
67.86/9.39	    inference('rw.lit', [status(esa)], [transitive_closure])).
67.86/9.39	thf(zip_derived_cl131, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i > $i > $o]:
67.86/9.39	                      (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 
67.86/9.39	                        X3 @ X2))))))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        |  (X0 @ X2 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ((X2) = ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ~ ('#form215' @ X1 @ X3))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl123, '10'])).
67.86/9.39	thf(zip_derived_cl133, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ (((((subrel @ '#sk1' @ ('#sk244' @ X3 @ X2)) & (trans @ 
67.86/9.39	              ('#sk244' @ X3 @ X2)))) =>
67.86/9.39	            ('#sk244' @ X3 @ X2 @ X3 @ X2)))
67.86/9.39	        | ~ ('#form215' @ X1 @ X3)
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ((X2) = ('#sk5' @ X2 @ X1))
67.86/9.39	        |  (X0 @ X2 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form84' @ X0))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl131])).
67.86/9.39	thf(zip_derived_cl137, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ ('#sk244' @ X3 @ X2 @ X3 @ X2)
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        |  (X0 @ X2 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ((X2) = ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ~ ('#form215' @ X1 @ X3))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])).
67.86/9.39	thf(zip_derived_cl38, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       (~ (tc @ '#sk1' @ '#sk3' @ X0)
67.86/9.39	        | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))),
67.86/9.39	    inference('lazy_cnf_or', [status(thm)], [zip_derived_cl33])).
67.86/9.39	thf(zip_derived_cl42, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       ( ('#form6' @ X0)
67.86/9.39	        | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl45, plain,
67.86/9.39	    (![X0 : $i]: (~ ('#form6' @ X0) | ~ (tc @ '#sk1' @ '#sk3' @ X0))),
67.86/9.39	    inference('renaming', [status(thm)], [zip_derived_cl38, zip_derived_cl42])).
67.86/9.39	thf(zip_derived_cl51, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i > $i > $o]:
67.86/9.39	                      (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 
67.86/9.39	                        '#sk3' @ X0))))))
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl45, '10'])).
67.86/9.39	thf(zip_derived_cl57, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       (~ (((((subrel @ '#sk1' @ ('#sk23' @ X0)) & (trans @ ('#sk23' @ X0)))) =>
67.86/9.39	            ('#sk23' @ X0 @ '#sk3' @ X0)))
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])).
67.86/9.39	thf(zip_derived_cl62, plain,
67.86/9.39	    (![X0 : $i]: (~ ('#sk23' @ X0 @ '#sk3' @ X0) | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])).
67.86/9.39	thf(zip_derived_cl43, plain,
67.86/9.39	    (![X0 : $i]: (~ (tc @ '#sk1' @ '#sk4' @ X0) |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])).
67.86/9.39	thf(zip_derived_cl52, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i > $i > $o]:
67.86/9.39	                      (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 
67.86/9.39	                        '#sk4' @ X0))))))
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl43, '10'])).
67.86/9.39	thf(zip_derived_cl58, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       (~ (((((subrel @ '#sk1' @ ('#sk24' @ X0)) & (trans @ ('#sk24' @ X0)))) =>
67.86/9.39	            ('#sk24' @ X0 @ '#sk4' @ X0)))
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl52])).
67.86/9.39	thf(zip_derived_cl64, plain,
67.86/9.39	    (![X0 : $i]: (~ ('#sk24' @ X0 @ '#sk4' @ X0) |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
67.86/9.39	thf(zip_derived_cl136, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       ( (((subrel @ '#sk1' @ ('#sk244' @ X3 @ X2)) & (trans @ 
67.86/9.39	           ('#sk244' @ X3 @ X2))))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        |  (X0 @ X2 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ((X2) = ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ~ ('#form215' @ X1 @ X3))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])).
67.86/9.39	thf(zip_derived_cl140, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       ( (subrel @ '#sk1' @ ('#sk244' @ X3 @ X2))
67.86/9.39	        | ~ ('#form215' @ X1 @ X3)
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ((X2) = ('#sk5' @ X2 @ X1))
67.86/9.39	        |  (X0 @ X2 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form84' @ X0))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl136])).
67.86/9.39	thf(subrel, axiom, (subrel @ X0 @ X1) =>
67.86/9.39	  ((((!!) @ (^[Y0 : $i]:
67.86/9.39	               (((!!) @ (^[Y1 : $i]: (((X0 @ Y0 @ Y1) => (X1 @ Y0 @ Y1)))))))))
67.86/9.39	   = ($true))).
67.86/9.39	thf('11', plain,
67.86/9.39	    (![X0:( $i > $i > $o ),X1:( $i > $i > $o )]:
67.86/9.39	     ( ( subrel @ X0 @ X1 ) <=>
67.86/9.39	       ( ![X6:$i,X8:$i]: ( ( X0 @ X6 @ X8 ) => ( X1 @ X6 @ X8 ) ) ) )),
67.86/9.39	    inference('rw.lit', [status(esa)], [subrel])).
67.86/9.39	thf(zip_derived_cl144, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                 ((('#sk1' @ Y0 @ Y1) => ('#sk244' @ X3 @ 
67.86/9.39	                                   X2 @ Y0 @ Y1)))))))))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        |  (X0 @ X2 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ((X2) = ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ~ ('#form215' @ X1 @ X3))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl140, '11'])).
67.86/9.39	thf(zip_derived_cl148, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       (~ ('#form84' @ X3)
67.86/9.39	        |  (((!!) @ (^[Y0 : $i]:
67.86/9.39	                       (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                   ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl149, plain,
67.86/9.39	    (![X3 : $i > $i > $o, X5 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]: ((('#sk1' @ X5 @ Y0) => (X3 @ X5 @ Y0))))))
67.86/9.39	        | ~ ('#form84' @ X3))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl148])).
67.86/9.39	thf(zip_derived_cl154, plain,
67.86/9.39	    (![X3 : $i > $i > $o, X5 : $i, X7 : $i]:
67.86/9.39	       ( ((('#sk1' @ X5 @ X7) => (X3 @ X5 @ X7))) | ~ ('#form84' @ X3))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl149])).
67.86/9.39	thf(zip_derived_cl158, plain,
67.86/9.39	    (![X3 : $i > $i > $o, X5 : $i, X7 : $i]:
67.86/9.39	       (~ ('#sk1' @ X5 @ X7) |  (X3 @ X5 @ X7) | ~ ('#form84' @ X3))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl154])).
67.86/9.39	thf(zip_derived_cl77, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( ('#form68' @ X3)
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    (((((X3 @ Y0 @ Y1) & (X3 @ 
67.86/9.39	                                        ('#sk49' @ X3) @ Y0))) =>
67.86/9.39	                                      (X3 @ ('#sk49' @ X3) @ Y1))))))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl78, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                      (((((X3 @ ('#sk69' @ X3) @ Y0) & (X3 @ 
67.86/9.39	                          ('#sk49' @ X3) @ ('#sk69' @ X3)))) =>
67.86/9.39	                        (X3 @ ('#sk49' @ X3) @ Y0))))))
67.86/9.39	        |  ('#form68' @ X3))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])).
67.86/9.39	thf(zip_derived_cl88, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       (~ (((((X3 @ ('#sk69' @ X3) @ ('#sk98' @ X3)) & (X3 @ 
67.86/9.39	              ('#sk49' @ X3) @ ('#sk69' @ X3)))) =>
67.86/9.39	            (X3 @ ('#sk49' @ X3) @ ('#sk98' @ X3))))
67.86/9.39	        |  ('#form68' @ X3))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl78])).
67.86/9.39	thf(zip_derived_cl97, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( (((X3 @ ('#sk69' @ X3) @ ('#sk98' @ X3)) & (X3 @ ('#sk49' @ X3) @ 
67.86/9.39	           ('#sk69' @ X3))))
67.86/9.39	        |  ('#form68' @ X3))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])).
67.86/9.39	thf(zip_derived_cl108, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( (X3 @ ('#sk69' @ X3) @ ('#sk98' @ X3)) |  ('#form68' @ X3))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl97])).
67.86/9.39	thf(zip_derived_cl61, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       ( (((subrel @ '#sk1' @ ('#sk23' @ X0)) & (trans @ ('#sk23' @ X0))))
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])).
67.86/9.39	thf(zip_derived_cl67, plain,
67.86/9.39	    (![X0 : $i]: ( (subrel @ '#sk1' @ ('#sk23' @ X0)) | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])).
67.86/9.39	thf(zip_derived_cl73, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                 ((('#sk1' @ Y0 @ Y1) => ('#sk23' @ X0 @ 
67.86/9.39	                                   Y0 @ Y1)))))))))
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl67, '11'])).
67.86/9.39	thf(zip_derived_cl81, plain,
67.86/9.39	    (![X0 : $i, X2 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     ((('#sk1' @ X2 @ Y0) => ('#sk23' @ X0 @ X2 @ Y0))))))
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl73])).
67.86/9.39	thf(zip_derived_cl91, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i]:
67.86/9.39	       ( ((('#sk1' @ X2 @ X4) => ('#sk23' @ X0 @ X2 @ X4)))
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl81])).
67.86/9.39	thf(zip_derived_cl101, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i]:
67.86/9.39	       (~ ('#sk1' @ X2 @ X4) |  ('#sk23' @ X0 @ X2 @ X4) | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])).
67.86/9.39	thf(zip_derived_cl68, plain,
67.86/9.39	    (![X0 : $i]: ( (trans @ ('#sk23' @ X0)) | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])).
67.86/9.39	thf(transitive, axiom, (trans @ X0) =>
67.86/9.39	  ((((!!) @ (^[Y0 : $i]:
67.86/9.39	               (((!!) @ (^[Y1 : $i]:
67.86/9.39	                           (((!!) @ (^[Y2 : $i]:
67.86/9.39	                                       (((((X0 @ Y1 @ Y2) & (X0 @ Y0 @ Y1))) =>
67.86/9.39	                                         (X0 @ Y0 @ Y2))))))))))))
67.86/9.39	   = ($true))).
67.86/9.39	thf('12', plain,
67.86/9.39	    (![X0:( $i > $i > $o )]:
67.86/9.39	     ( ( trans @ X0 ) <=>
67.86/9.39	       ( ![X5:$i,X7:$i,X9:$i]:
67.86/9.39	         ( ( ( X0 @ X7 @ X9 ) & ( X0 @ X5 @ X7 ) ) => ( X0 @ X5 @ X9 ) ) ) )),
67.86/9.39	    inference('rw.lit', [status(esa)], [transitive])).
67.86/9.39	thf(zip_derived_cl74, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                 (((!!) @ (^[Y2 : $i]:
67.86/9.39	                                             ((((('#sk23' @ X0 @ Y1 @ Y2) &
67.86/9.39	                                                 ('#sk23' @ X0 @ Y0 @ Y1))) =>
67.86/9.39	                                               ('#sk23' @ X0 @ Y0 @ Y2))))))))))))
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl68, '12'])).
67.86/9.39	thf(zip_derived_cl82, plain,
67.86/9.39	    (![X0 : $i, X2 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                 ((((('#sk23' @ X0 @ Y0 @ Y1) & ('#sk23' @ 
67.86/9.39	                                     X0 @ X2 @ Y0))) =>
67.86/9.39	                                   ('#sk23' @ X0 @ X2 @ Y1)))))))))
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl74])).
67.86/9.39	thf(zip_derived_cl92, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     ((((('#sk23' @ X0 @ X4 @ Y0) & ('#sk23' @ X0 @ X2 @ X4))) =>
67.86/9.39	                       ('#sk23' @ X0 @ X2 @ Y0))))))
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl82])).
67.86/9.39	thf(zip_derived_cl102, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]:
67.86/9.39	       ( ((((('#sk23' @ X0 @ X4 @ X6) & ('#sk23' @ X0 @ X2 @ X4))) =>
67.86/9.39	           ('#sk23' @ X0 @ X2 @ X6)))
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl92])).
67.86/9.39	thf(zip_derived_cl111, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]:
67.86/9.39	       (~ ((('#sk23' @ X0 @ X4 @ X6) & ('#sk23' @ X0 @ X2 @ X4)))
67.86/9.39	        |  ('#sk23' @ X0 @ X2 @ X6)
67.86/9.39	        | ~ ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])).
67.86/9.39	thf(zip_derived_cl115, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]:
67.86/9.39	       (~ ('#sk23' @ X0 @ X4 @ X6)
67.86/9.39	        | ~ ('#sk23' @ X0 @ X2 @ X4)
67.86/9.39	        | ~ ('#form6' @ X0)
67.86/9.39	        |  ('#sk23' @ X0 @ X2 @ X6))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])).
67.86/9.39	thf(zip_derived_cl15, plain,
67.86/9.39	    ( ((('#sk1' @ '#sk2' @ '#sk3') & ('#sk1' @ '#sk2' @ '#sk4')))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])).
67.86/9.39	thf(zip_derived_cl19, plain, ( ('#sk1' @ '#sk2' @ '#sk4')),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl15])).
67.86/9.39	thf(zip_derived_cl114, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2)))))
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ((X1) = ('#sk5' @ X2 @ X1))
67.86/9.39	        |  (X0 @ X1 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        | ~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1))))))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl110, '3'])).
67.86/9.39	thf(zip_derived_cl119, plain,
67.86/9.39	    (![X2 : $i, X3 : $i]:
67.86/9.39	       ( ('#form215' @ X2 @ X3)
67.86/9.39	        | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl122, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ ('#form215' @ X2 @ X3)
67.86/9.39	        | ~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1)))))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        |  (X0 @ X1 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ((X1) = ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form68' @ X0))),
67.86/9.39	    inference('renaming', [status(thm)],
67.86/9.39	              [zip_derived_cl114, zip_derived_cl119])).
67.86/9.39	thf(zip_derived_cl119, plain,
67.86/9.39	    (![X2 : $i, X3 : $i]:
67.86/9.39	       ( ('#form215' @ X2 @ X3)
67.86/9.39	        | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl127, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       (~ ('#form215' @ X1 @ X3)
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ((X1) = ('#sk5' @ X2 @ X1))
67.86/9.39	        |  (X0 @ X1 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        | ~ ('#form215' @ X2 @ X3))),
67.86/9.39	    inference('renaming', [status(thm)],
67.86/9.39	              [zip_derived_cl122, zip_derived_cl119])).
67.86/9.39	thf(zip_derived_cl85, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( ('#form84' @ X3)
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl86, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                      ((('#sk1' @ ('#sk85' @ X3) @ Y0) => (X3 @ 
67.86/9.39	                        ('#sk85' @ X3) @ Y0))))))
67.86/9.39	        |  ('#form84' @ X3))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl85])).
67.86/9.39	thf(zip_derived_cl96, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       (~ ((('#sk1' @ ('#sk85' @ X3) @ ('#sk118' @ X3)) => (X3 @ 
67.86/9.39	            ('#sk85' @ X3) @ ('#sk118' @ X3))))
67.86/9.39	        |  ('#form84' @ X3))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])).
67.86/9.39	thf(zip_derived_cl106, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( ('#sk1' @ ('#sk85' @ X3) @ ('#sk118' @ X3)) |  ('#form84' @ X3))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])).
67.86/9.39	thf(zip_derived_cl107, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       (~ (X3 @ ('#sk85' @ X3) @ ('#sk118' @ X3)) |  ('#form84' @ X3))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])).
67.86/9.39	thf(zip_derived_cl98, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       (~ (X3 @ ('#sk49' @ X3) @ ('#sk98' @ X3)) |  ('#form68' @ X3))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])).
67.86/9.39	thf(zip_derived_cl109, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( (X3 @ ('#sk49' @ X3) @ ('#sk69' @ X3)) |  ('#form68' @ X3))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl97])).
67.86/9.39	thf(zip_derived_cl18, plain, ( ('#sk1' @ '#sk2' @ '#sk3')),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl15])).
67.86/9.39	thf(zip_derived_cl144, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                 ((('#sk1' @ Y0 @ Y1) => ('#sk244' @ X3 @ 
67.86/9.39	                                   X2 @ Y0 @ Y1)))))))))
67.86/9.39	        | ~ ('#form84' @ X0)
67.86/9.39	        |  (X0 @ X2 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ((X2) = ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ~ ('#form215' @ X1 @ X3))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl140, '11'])).
67.86/9.39	thf(zip_derived_cl148, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       (~ ('#form84' @ X3)
67.86/9.39	        |  (((!!) @ (^[Y0 : $i]:
67.86/9.39	                       (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                   ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl85, plain,
67.86/9.39	    (![X3 : $i > $i > $o]:
67.86/9.39	       ( ('#form84' @ X3)
67.86/9.39	        | ~ (((!!) @ (^[Y0 : $i]:
67.86/9.39	                        (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                    ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl150, plain,
67.86/9.39	    (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]:
67.86/9.39	       ( ('#form84' @ ('#sk244' @ X3 @ X2))
67.86/9.39	        | ~ ('#form215' @ X1 @ X3)
67.86/9.39	        | ~ ('#form68' @ X0)
67.86/9.39	        | ((X2) = ('#sk5' @ X2 @ X1))
67.86/9.39	        |  (X0 @ X2 @ ('#sk5' @ X2 @ X1))
67.86/9.39	        | ~ ('#form84' @ X0))),
67.86/9.39	    inference('renaming', [status(thm)],
67.86/9.39	              [zip_derived_cl144, zip_derived_cl148, zip_derived_cl85])).
67.86/9.39	thf(zip_derived_cl63, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       ( (((subrel @ '#sk1' @ ('#sk24' @ X0)) & (trans @ ('#sk24' @ X0))))
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
67.86/9.39	thf(zip_derived_cl69, plain,
67.86/9.39	    (![X0 : $i]: ( (subrel @ '#sk1' @ ('#sk24' @ X0)) |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])).
67.86/9.39	thf(zip_derived_cl75, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                 ((('#sk1' @ Y0 @ Y1) => ('#sk24' @ X0 @ 
67.86/9.39	                                   Y0 @ Y1)))))))))
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl69, '11'])).
67.86/9.39	thf(zip_derived_cl83, plain,
67.86/9.39	    (![X0 : $i, X2 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     ((('#sk1' @ X2 @ Y0) => ('#sk24' @ X0 @ X2 @ Y0))))))
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl75])).
67.86/9.39	thf(zip_derived_cl93, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i]:
67.86/9.39	       ( ((('#sk1' @ X2 @ X4) => ('#sk24' @ X0 @ X2 @ X4)))
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl83])).
67.86/9.39	thf(zip_derived_cl103, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i]:
67.86/9.39	       (~ ('#sk1' @ X2 @ X4) |  ('#sk24' @ X0 @ X2 @ X4) |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl93])).
67.86/9.39	thf(zip_derived_cl70, plain,
67.86/9.39	    (![X0 : $i]: ( (trans @ ('#sk24' @ X0)) |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])).
67.86/9.39	thf(zip_derived_cl76, plain,
67.86/9.39	    (![X0 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                 (((!!) @ (^[Y2 : $i]:
67.86/9.39	                                             ((((('#sk24' @ X0 @ Y1 @ Y2) &
67.86/9.39	                                                 ('#sk24' @ X0 @ Y0 @ Y1))) =>
67.86/9.39	                                               ('#sk24' @ X0 @ Y0 @ Y2))))))))))))
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl70, '12'])).
67.86/9.39	thf(zip_derived_cl84, plain,
67.86/9.39	    (![X0 : $i, X2 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                 ((((('#sk24' @ X0 @ Y0 @ Y1) & ('#sk24' @ 
67.86/9.39	                                     X0 @ X2 @ Y0))) =>
67.86/9.39	                                   ('#sk24' @ X0 @ X2 @ Y1)))))))))
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])).
67.86/9.39	thf(zip_derived_cl94, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     ((((('#sk24' @ X0 @ X4 @ Y0) & ('#sk24' @ X0 @ X2 @ X4))) =>
67.86/9.39	                       ('#sk24' @ X0 @ X2 @ Y0))))))
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])).
67.86/9.39	thf(zip_derived_cl104, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]:
67.86/9.39	       ( ((((('#sk24' @ X0 @ X4 @ X6) & ('#sk24' @ X0 @ X2 @ X4))) =>
67.86/9.39	           ('#sk24' @ X0 @ X2 @ X6)))
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])).
67.86/9.39	thf(zip_derived_cl112, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]:
67.86/9.39	       (~ ((('#sk24' @ X0 @ X4 @ X6) & ('#sk24' @ X0 @ X2 @ X4)))
67.86/9.39	        |  ('#sk24' @ X0 @ X2 @ X6)
67.86/9.39	        |  ('#form6' @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])).
67.86/9.39	thf(zip_derived_cl116, plain,
67.86/9.39	    (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]:
67.86/9.39	       (~ ('#sk24' @ X0 @ X4 @ X6)
67.86/9.39	        | ~ ('#sk24' @ X0 @ X2 @ X4)
67.86/9.39	        |  ('#form6' @ X0)
67.86/9.39	        |  ('#sk24' @ X0 @ X2 @ X6))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl112])).
67.86/9.39	thf(zip_derived_cl119, plain,
67.86/9.39	    (![X2 : $i, X3 : $i]:
67.86/9.39	       ( ('#form215' @ X2 @ X3)
67.86/9.39	        | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))))),
67.86/9.39	    define([status(thm)])).
67.86/9.39	thf(zip_derived_cl120, plain,
67.86/9.39	    (![X2 : $i, X3 : $i]:
67.86/9.39	       (~ (tc @ '#sk1' @ X3 @ X2) |  ('#form215' @ X2 @ X3))),
67.86/9.39	    inference('lazy_cnf_or', [status(thm)], [zip_derived_cl119])).
67.86/9.39	thf(zip_derived_cl128, plain,
67.86/9.39	    (![X0 : $i, X1 : $i]:
67.86/9.39	       (~ (((!!) @ (^[Y0 : $i > $i > $o]:
67.86/9.39	                      (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 
67.86/9.39	                        X0 @ X1))))))
67.86/9.39	        |  ('#form215' @ X1 @ X0))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl120, '10'])).
67.86/9.39	thf(zip_derived_cl132, plain,
67.86/9.39	    (![X0 : $i, X1 : $i]:
67.86/9.39	       (~ (((((subrel @ '#sk1' @ ('#sk244' @ X0 @ X1)) & (trans @ 
67.86/9.39	              ('#sk244' @ X0 @ X1)))) =>
67.86/9.39	            ('#sk244' @ X0 @ X1 @ X0 @ X1)))
67.86/9.39	        |  ('#form215' @ X1 @ X0))),
67.86/9.39	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl128])).
67.86/9.39	thf(zip_derived_cl135, plain,
67.86/9.39	    (![X0 : $i, X1 : $i]:
67.86/9.39	       (~ ('#sk244' @ X0 @ X1 @ X0 @ X1) |  ('#form215' @ X1 @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl132])).
67.86/9.39	thf(zip_derived_cl134, plain,
67.86/9.39	    (![X0 : $i, X1 : $i]:
67.86/9.39	       ( (((subrel @ '#sk1' @ ('#sk244' @ X0 @ X1)) & (trans @ 
67.86/9.39	           ('#sk244' @ X0 @ X1))))
67.86/9.39	        |  ('#form215' @ X1 @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl132])).
67.86/9.39	thf(zip_derived_cl138, plain,
67.86/9.39	    (![X0 : $i, X1 : $i]:
67.86/9.39	       ( (subrel @ '#sk1' @ ('#sk244' @ X0 @ X1)) |  ('#form215' @ X1 @ X0))),
67.86/9.39	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl134])).
67.86/9.39	thf(zip_derived_cl142, plain,
67.86/9.39	    (![X0 : $i, X1 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     (((!!) @ (^[Y1 : $i]:
67.86/9.39	                                 ((('#sk1' @ Y0 @ Y1) => ('#sk244' @ X0 @ 
67.86/9.39	                                   X1 @ Y0 @ Y1)))))))))
67.86/9.39	        |  ('#form215' @ X1 @ X0))),
67.86/9.39	    inference('rw_clause', [status(thm)], [zip_derived_cl138, '11'])).
67.86/9.39	thf(zip_derived_cl146, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X3 : $i]:
67.86/9.39	       ( (((!!) @ (^[Y0 : $i]:
67.86/9.39	                     ((('#sk1' @ X3 @ Y0) => ('#sk244' @ X0 @ X1 @ X3 @ Y0))))))
67.86/9.39	        |  ('#form215' @ X1 @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl142])).
67.86/9.39	thf(zip_derived_cl152, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X3 : $i, X5 : $i]:
67.86/9.39	       ( ((('#sk1' @ X3 @ X5) => ('#sk244' @ X0 @ X1 @ X3 @ X5)))
67.86/9.39	        |  ('#form215' @ X1 @ X0))),
67.86/9.39	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl146])).
67.86/9.39	thf(zip_derived_cl156, plain,
67.86/9.39	    (![X0 : $i, X1 : $i, X3 : $i, X5 : $i]:
67.86/9.39	       (~ ('#sk1' @ X3 @ X5)
67.86/9.39	        |  ('#sk244' @ X0 @ X1 @ X3 @ X5)
67.86/9.39	        |  ('#form215' @ X1 @ X0))),
67.86/9.39	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl152])).
67.86/9.39	thf(zip_derived_cl7637, plain, ($false),
67.86/9.39	    inference('eprover', [status(thm)],
67.86/9.39	              [zip_derived_cl48, zip_derived_cl54, zip_derived_cl137, 
67.86/9.39	               zip_derived_cl62, zip_derived_cl64, zip_derived_cl158, 
67.86/9.39	               zip_derived_cl108, zip_derived_cl101, zip_derived_cl115, 
67.86/9.39	               zip_derived_cl19, zip_derived_cl127, zip_derived_cl106, 
67.86/9.39	               zip_derived_cl107, zip_derived_cl98, zip_derived_cl109, 
67.86/9.39	               zip_derived_cl18, zip_derived_cl150, zip_derived_cl103, 
67.86/9.39	               zip_derived_cl116, zip_derived_cl135, zip_derived_cl156])).
67.86/9.39	
67.86/9.39	% SZS output end Refutation
67.86/9.39	
67.86/9.39	
67.86/9.39	% Terminating...
68.41/9.48	% Runner terminated.
68.41/9.49	% Zipperpin 1.5 exiting
68.41/9.49	EOF