0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.14	% Command    : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.xKlxAy7Fcw true
0.13/0.35	% Computer   : n027.cluster.edu
0.13/0.35	% Model      : x86_64 x86_64
0.13/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory     : 8042.1875MB
0.13/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 1200
0.13/0.35	% WCLimit    : 120
0.13/0.35	% DateTime   : Tue Jul 13 11:21:25 EDT 2021
0.13/0.35	% CPUTime    : 
0.13/0.35	% Running portfolio for 120 s
0.13/0.35	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.13/0.35	% Number of cores: 8
0.13/0.35	% Python version: Python 3.6.8
0.13/0.35	% Running in HO mode
0.53/0.66	% Total configuration time : 828
0.53/0.66	% Estimated wc time : 983
0.53/0.66	% Estimated cpu time (8 cpus) : 122.875
0.53/0.73	% /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s
0.53/0.74	% /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s
0.53/0.75	% /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s
0.53/0.75	% /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s
0.53/0.75	% /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s
0.53/0.75	% /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s
0.55/0.76	% /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s
0.55/0.76	% /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s
77.29/10.38	% Solved by lams/40_c.s.sh.
77.29/10.38	% running E: timeout 32 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.xKlxAy7Fcw/e_inputffcc64 --cpu-limit=30 --auto-schedule -s -p
77.29/10.38	% done 362 iterations in 9.576s
77.29/10.38	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
77.29/10.38	% SZS output start Refutation
77.29/10.38	thf('#l_lift2063_type', type, '#l_lift2063': $i > $o).
77.29/10.38	thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
77.29/10.38	thf(or3_type, type, or3: $o > $o > $o > $o).
77.29/10.38	thf(n_is_type, type, n_is: $i > $i > $o).
77.29/10.38	thf(sk__4_type, type, sk__4: $i).
77.29/10.38	thf(n_1_type, type, n_1: $i).
77.29/10.38	thf(l_or_type, type, l_or: $o > $o > $o).
77.29/10.38	thf(sk__2_type, type, sk__2: $i).
77.29/10.38	thf(moreis_type, type, moreis: $i > $i > $o).
77.29/10.38	thf(nis_type, type, nis: $i > $i > $o).
77.29/10.38	thf('#l_lift2064_type', type, '#l_lift2064': $i > $o).
77.29/10.38	thf(in_type, type, in: $i > $i > $o).
77.29/10.38	thf(imp_type, type, imp: $o > $o > $o).
77.29/10.38	thf(sk__3_type, type, sk__3: $i).
77.29/10.38	thf('#l_lift2065_type', type, '#l_lift2065': $i > $i > $o).
77.29/10.38	thf(lessis_type, type, lessis: $i > $i > $o).
77.29/10.38	thf(nat_type, type, nat: $i).
77.29/10.38	thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
77.29/10.38	thf(e_is_type, type, e_is: $i > $i > $i > $o).
77.29/10.38	thf(n_some_type, type, n_some: ($i > $o) > $o).
77.29/10.38	thf(ordsucc_type, type, ordsucc: $i > $i).
77.29/10.38	thf(iii_type, type, iii: $i > $i > $o).
77.29/10.38	thf(omega_type, type, omega: $i).
77.29/10.38	thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
77.29/10.38	thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
77.29/10.38	thf(d_not_type, type, d_not: $o > $o).
77.29/10.38	thf(emptyset_type, type, emptyset: $i).
77.29/10.38	thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
77.29/10.38	thf(def_moreis, axiom,(( moreis  ) =
77.29/10.38	  (^[X0:$i,X1:$i]: ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) )))).
77.29/10.38	thf(def_d_29_ii, axiom,(( d_29_ii  ) =
77.29/10.38	  (^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X0 @ X1 ) )))).
77.29/10.38	thf('0', plain,
77.29/10.38	    (( d_29_ii ) = ( ^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)], [def_d_29_ii])).
77.29/10.38	thf('1', plain,
77.29/10.38	    (( d_29_ii ) =
77.29/10.38	     ( ^[V_1:$i,V_2:$i]: ( n_some @ ( diffprop @ V_1 @ V_2 ) ) )),
77.29/10.38	    define([status(thm)])).thf(def_n_is, axiom,(( n_is  ) = (e_is @ nat))).
77.29/10.38	thf(def_nat, axiom,(( nat  ) =
77.29/10.38	  (d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) )))).
77.29/10.38	thf('2', plain,
77.29/10.38	    (( nat ) = ( d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)], [def_nat])).
77.29/10.38	thf('3', plain,
77.29/10.38	    (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(def_e_is, axiom,(( e_is  ) = (^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) )))).
77.29/10.38	thf('4', plain, (( e_is ) = ( ^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)], [def_e_is])).
77.29/10.38	thf('5', plain,
77.29/10.38	    (( e_is ) = ( ^[V_1:$i,V_2:$i,V_3:$i]: ( ( V_2 ) = ( V_3 ) ) )),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf('6', plain, (( n_is ) = ( e_is @ nat )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)], [def_n_is, '3', '5'])).
77.29/10.38	thf('7', plain, (( n_is ) = ( e_is @ nat )), define([status(thm)])).
77.29/10.38	thf(def_l_or, axiom,(( l_or  ) = (^[X0:$o]: ( imp @ ( d_not @ X0 ) )))).
77.29/10.38	thf(def_d_not, axiom,(( d_not  ) = (^[X0:$o]: ( imp @ X0 @ $false )))).
77.29/10.38	thf(def_imp, axiom,(( imp  ) = (^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) )))).
77.29/10.38	thf('8', plain, (( imp ) = ( ^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)], [def_imp])).
77.29/10.38	thf('9', plain, (( imp ) = ( ^[V_1:$o,V_2:$o]: ( ( V_1 ) => ( V_2 ) ) )),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf('10', plain, (( d_not ) = ( ^[X0:$o]: ( imp @ X0 @ $false ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)], [def_d_not, '9'])).
77.29/10.38	thf('11', plain, (( d_not ) = ( ^[V_1:$o]: ( imp @ V_1 @ $false ) )),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf('12', plain, (( l_or ) = ( ^[X0:$o]: ( imp @ ( d_not @ X0 ) ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)], [def_l_or, '11', '9'])).
77.29/10.38	thf('13', plain, (( l_or ) = ( ^[V_1:$o]: ( imp @ ( d_not @ V_1 ) ) )),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf('14', plain,
77.29/10.38	    (( moreis ) =
77.29/10.38	     ( ^[X0:$i,X1:$i]: ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)],
77.29/10.38	              [def_moreis, '1', '7', '3', '5', '13', '11', '9'])).
77.29/10.38	thf('15', plain,
77.29/10.38	    (( moreis ) =
77.29/10.38	     ( ^[V_1:$i,V_2:$i]:
77.29/10.38	       ( l_or @ ( d_29_ii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) )),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(def_all_of, axiom,(( all_of  ) =
77.29/10.38	  (^[X0:( $i > $o ),X1:( $i > $o )]:
77.29/10.38	   ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))).
77.29/10.38	thf('16', plain,
77.29/10.38	    (( all_of ) =
77.29/10.38	     ( ^[X0:( $i > $o ),X1:( $i > $o )]:
77.29/10.38	       ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)], [def_all_of])).
77.29/10.38	thf('17', plain,
77.29/10.38	    (( all_of ) =
77.29/10.38	     ( ^[V_1:( $i > $o ),V_2:( $i > $o )]:
77.29/10.38	       ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(satz16d, conjecture,
77.29/10.38	  (all_of @
77.29/10.38	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
77.29/10.38	   ( ^[X0:$i]:
77.29/10.38	     ( all_of @
77.29/10.38	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
77.29/10.38	       ( ^[X1:$i]:
77.29/10.38	         ( all_of @
77.29/10.38	           ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 
77.29/10.38	           ( ^[X2:$i]:
77.29/10.38	             ( ( d_29_ii @ X0 @ X1 ) =>
77.29/10.38	               ( ( moreis @ X1 @ X2 ) => ( d_29_ii @ X0 @ X2 ) ) ) ) ) ) ) ))).
77.29/10.38	thf(zf_stmt_0, conjecture,
77.29/10.38	  (![X4:$i]:
77.29/10.38	   ( ( is_of @
77.29/10.38	       X4 @ 
77.29/10.38	       ( ^[V_1:$i]:
77.29/10.38	         ( in @
77.29/10.38	           V_1 @ 
77.29/10.38	           ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	     ( ![X6:$i]:
77.29/10.38	       ( ( is_of @
77.29/10.38	           X6 @ 
77.29/10.38	           ( ^[V_3:$i]:
77.29/10.38	             ( in @
77.29/10.38	               V_3 @ 
77.29/10.38	               ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	         ( ![X8:$i]:
77.29/10.38	           ( ( is_of @
77.29/10.38	               X8 @ 
77.29/10.38	               ( ^[V_5:$i]:
77.29/10.38	                 ( in @
77.29/10.38	                   V_5 @ 
77.29/10.38	                   ( d_Sep @
77.29/10.38	                     omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	             ( ( n_some @ ( diffprop @ X4 @ X6 ) ) =>
77.29/10.38	               ( ( ( ~( n_some @ ( diffprop @ X6 @ X8 ) ) ) =>
77.29/10.38	                   ( ( X6 ) = ( X8 ) ) ) =>
77.29/10.38	                 ( n_some @ ( diffprop @ X4 @ X8 ) ) ) ) ) ) ) ) ))).
77.29/10.38	thf(zf_stmt_1, negated_conjecture,
77.29/10.38	  (~( ![X4:$i]:
77.29/10.38	      ( ( is_of @
77.29/10.38	          X4 @ 
77.29/10.38	          ( ^[V_1:$i]:
77.29/10.38	            ( in @
77.29/10.38	              V_1 @ 
77.29/10.38	              ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	        ( ![X6:$i]:
77.29/10.38	          ( ( is_of @
77.29/10.38	              X6 @ 
77.29/10.38	              ( ^[V_3:$i]:
77.29/10.38	                ( in @
77.29/10.38	                  V_3 @ 
77.29/10.38	                  ( d_Sep @
77.29/10.38	                    omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	            ( ![X8:$i]:
77.29/10.38	              ( ( is_of @
77.29/10.38	                  X8 @ 
77.29/10.38	                  ( ^[V_5:$i]:
77.29/10.38	                    ( in @
77.29/10.38	                      V_5 @ 
77.29/10.38	                      ( d_Sep @
77.29/10.38	                        omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	                ( ( n_some @ ( diffprop @ X4 @ X6 ) ) =>
77.29/10.38	                  ( ( ( ~( n_some @ ( diffprop @ X6 @ X8 ) ) ) =>
77.29/10.38	                      ( ( X6 ) = ( X8 ) ) ) =>
77.29/10.38	                    ( n_some @ ( diffprop @ X4 @ X8 ) ) ) ) ) ) ) ) ) )),
77.29/10.38	  inference('cnf.neg', [status(esa)], [zf_stmt_0])).
77.29/10.38	thf(zip_derived_cl59, plain, ( (n_some @ (diffprop @ sk__2 @ sk__3))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_1])).
77.29/10.38	thf(zip_derived_cl57, plain,
77.29/10.38	    ((((sk__3) = (sk__4)) |  (n_some @ (diffprop @ sk__3 @ sk__4)))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_1])).
77.29/10.38	thf(zip_derived_cl60, plain,
77.29/10.38	    ( (is_of @ sk__3 @ 
77.29/10.38	       (^[Y0 : $i]:
77.29/10.38	          (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_1])).
77.29/10.38	thf(refis, axiom,
77.29/10.38	  (![X0:$i]:
77.29/10.38	   ( all_of @
77.29/10.38	     ( ^[X1:$i]: ( in @ X1 @ X0 ) ) @ ( ^[X1:$i]: ( e_is @ X0 @ X1 @ X1 ) ) ))).
77.29/10.38	thf(zf_stmt_2, axiom,
77.29/10.38	  (![X4:$i,X6:$i]:
77.29/10.38	   ( ( is_of @ X6 @ ( ^[V_1:$i]: ( in @ V_1 @ X4 ) ) ) => ( ( X6 ) = ( X6 ) ) ))).
77.29/10.38	thf(zip_derived_cl3, plain,
77.29/10.38	    (![X0 : $i, X1 : $i]:
77.29/10.38	       ($true | ~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ X1))))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_2])).
77.29/10.38	thf(zip_derived_cl3431, plain,
77.29/10.38	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(def_n_1, axiom,(( n_1  ) = (ordsucc @ emptyset))).
77.29/10.38	thf('18', plain, (( n_1 ) = ( ordsucc @ emptyset )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)], [def_n_1])).
77.29/10.38	thf('19', plain, (( n_1 ) = ( ordsucc @ emptyset )), define([status(thm)])).
77.29/10.38	thf(def_nis, axiom,(( nis  ) =
77.29/10.38	  (^[X0:$i,X1:$i]: ( d_not @ ( n_is @ X0 @ X1 ) )))).
77.29/10.38	thf('20', plain,
77.29/10.38	    (( nis ) = ( ^[X0:$i,X1:$i]: ( d_not @ ( n_is @ X0 @ X1 ) ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)],
77.29/10.38	              [def_nis, '7', '3', '5', '11', '9'])).
77.29/10.38	thf('21', plain,
77.29/10.38	    (( nis ) = ( ^[V_1:$i,V_2:$i]: ( d_not @ ( n_is @ V_1 @ V_2 ) ) )),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(n_ax3, axiom,
77.29/10.38	  (all_of @
77.29/10.38	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
77.29/10.38	   ( ^[X0:$i]: ( nis @ ( ordsucc @ X0 ) @ n_1 ) ))).
77.29/10.38	thf(zf_stmt_3, axiom,
77.29/10.38	  (![X4:$i]:
77.29/10.38	   ( ( is_of @
77.29/10.38	       X4 @ 
77.29/10.38	       ( ^[V_1:$i]:
77.29/10.38	         ( in @
77.29/10.38	           V_1 @ 
77.29/10.38	           ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	     ( ( ordsucc @ X4 ) != ( ordsucc @ emptyset ) ) ))).
77.29/10.38	thf(zip_derived_cl1, plain,
77.29/10.38	    (![X0 : $i]:
77.29/10.38	       (((ordsucc @ X0) != (ordsucc @ emptyset))
77.29/10.38	        | ~ (is_of @ X0 @ 
77.29/10.38	             (^[Y0 : $i]:
77.29/10.38	                (in @ Y0 @ 
77.29/10.38	                 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_3])).
77.29/10.38	thf(zip_derived_cl3428, plain,
77.29/10.38	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3482, plain,
77.29/10.38	    ( (is_of @ sk__3 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')))),
77.29/10.38	    inference('lambda_lifting', [status(thm)],
77.29/10.38	              [zip_derived_cl60, zip_derived_cl3431, zip_derived_cl3428])).
77.29/10.38	thf(satz10h, axiom,
77.29/10.38	  (all_of @
77.29/10.38	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
77.29/10.38	   ( ^[X0:$i]:
77.29/10.38	     ( all_of @
77.29/10.38	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
77.29/10.38	       ( ^[X1:$i]: ( ( iii @ X0 @ X1 ) => ( d_not @ ( moreis @ X0 @ X1 ) ) ) ) ) ))).
77.29/10.38	thf(zf_stmt_4, axiom,
77.29/10.38	  (![X4:$i]:
77.29/10.38	   ( ( is_of @
77.29/10.38	       X4 @ 
77.29/10.38	       ( ^[V_1:$i]:
77.29/10.38	         ( in @
77.29/10.38	           V_1 @ 
77.29/10.38	           ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	     ( ![X6:$i]:
77.29/10.38	       ( ( is_of @
77.29/10.38	           X6 @ 
77.29/10.38	           ( ^[V_3:$i]:
77.29/10.38	             ( in @
77.29/10.38	               V_3 @ 
77.29/10.38	               ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	         ( ( iii @ X4 @ X6 ) =>
77.29/10.38	           ( ~( ( ~( n_some @ ( diffprop @ X4 @ X6 ) ) ) =>
77.29/10.38	                ( ( X4 ) = ( X6 ) ) ) ) ) ) ) ))).
77.29/10.38	thf(zip_derived_cl52, plain,
77.29/10.38	    (![X0 : $i, X1 : $i]:
77.29/10.38	       (~ (is_of @ X0 @ 
77.29/10.38	           (^[Y0 : $i]:
77.29/10.38	              (in @ Y0 @ 
77.29/10.38	               (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))
77.29/10.38	        | ~ (n_some @ (diffprop @ X1 @ X0))
77.29/10.38	        | ~ (iii @ X1 @ X0)
77.29/10.38	        | ~ (is_of @ X1 @ 
77.29/10.38	             (^[Y0 : $i]:
77.29/10.38	                (in @ Y0 @ 
77.29/10.38	                 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_4])).
77.29/10.38	thf(zip_derived_cl3431, plain,
77.29/10.38	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3428, plain,
77.29/10.38	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3431, plain,
77.29/10.38	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3428, plain,
77.29/10.38	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3477, plain,
77.29/10.38	    (![X0 : $i, X1 : $i]:
77.29/10.38	       (~ (is_of @ X0 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')))
77.29/10.38	        | ~ (n_some @ (diffprop @ X1 @ X0))
77.29/10.38	        | ~ (iii @ X1 @ X0)
77.29/10.38	        | ~ (is_of @ X1 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063'))))),
77.29/10.38	    inference('lambda_lifting', [status(thm)],
77.29/10.38	              [zip_derived_cl52, zip_derived_cl3431, zip_derived_cl3428, 
77.29/10.38	               zip_derived_cl3431, zip_derived_cl3428])).
77.29/10.38	thf(def_lessis, axiom,(( lessis  ) =
77.29/10.38	  (^[X0:$i,X1:$i]: ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) )))).
77.29/10.38	thf('22', plain,
77.29/10.38	    (( lessis ) =
77.29/10.38	     ( ^[X0:$i,X1:$i]: ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)],
77.29/10.38	              [def_lessis, '7', '3', '5', '13', '11', '9'])).
77.29/10.38	thf('23', plain,
77.29/10.38	    (( lessis ) =
77.29/10.38	     ( ^[V_1:$i,V_2:$i]:
77.29/10.38	       ( l_or @ ( iii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) )),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(satz10g, axiom,
77.29/10.38	  (all_of @
77.29/10.38	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
77.29/10.38	   ( ^[X0:$i]:
77.29/10.38	     ( all_of @
77.29/10.38	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
77.29/10.38	       ( ^[X1:$i]:
77.29/10.38	         ( ( d_29_ii @ X0 @ X1 ) => ( d_not @ ( lessis @ X0 @ X1 ) ) ) ) ) ))).
77.29/10.38	thf(zf_stmt_5, axiom,
77.29/10.38	  (![X4:$i]:
77.29/10.38	   ( ( is_of @
77.29/10.38	       X4 @ 
77.29/10.38	       ( ^[V_1:$i]:
77.29/10.38	         ( in @
77.29/10.38	           V_1 @ 
77.29/10.38	           ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	     ( ![X6:$i]:
77.29/10.38	       ( ( is_of @
77.29/10.38	           X6 @ 
77.29/10.38	           ( ^[V_3:$i]:
77.29/10.38	             ( in @
77.29/10.38	               V_3 @ 
77.29/10.38	               ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.38	         ( ( n_some @ ( diffprop @ X4 @ X6 ) ) =>
77.29/10.38	           ( ~( ( ~( iii @ X4 @ X6 ) ) => ( ( X4 ) = ( X6 ) ) ) ) ) ) ) ))).
77.29/10.38	thf(zip_derived_cl51, plain,
77.29/10.38	    (![X0 : $i, X1 : $i]:
77.29/10.38	       (~ (is_of @ X0 @ 
77.29/10.38	           (^[Y0 : $i]:
77.29/10.38	              (in @ Y0 @ 
77.29/10.38	               (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))
77.29/10.38	        | ((X1) != (X0))
77.29/10.38	        | ~ (n_some @ (diffprop @ X1 @ X0))
77.29/10.38	        | ~ (is_of @ X1 @ 
77.29/10.38	             (^[Y0 : $i]:
77.29/10.38	                (in @ Y0 @ 
77.29/10.38	                 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_5])).
77.29/10.38	thf(zip_derived_cl3431, plain,
77.29/10.38	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3428, plain,
77.29/10.38	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3431, plain,
77.29/10.38	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3428, plain,
77.29/10.38	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3476, plain,
77.29/10.38	    (![X0 : $i, X1 : $i]:
77.29/10.38	       (~ (is_of @ X0 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')))
77.29/10.38	        | ((X1) != (X0))
77.29/10.38	        | ~ (n_some @ (diffprop @ X1 @ X0))
77.29/10.38	        | ~ (is_of @ X1 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063'))))),
77.29/10.38	    inference('lambda_lifting', [status(thm)],
77.29/10.38	              [zip_derived_cl51, zip_derived_cl3431, zip_derived_cl3428, 
77.29/10.38	               zip_derived_cl3431, zip_derived_cl3428])).
77.29/10.38	thf(zip_derived_cl55, plain,
77.29/10.38	    ( (is_of @ sk__2 @ 
77.29/10.38	       (^[Y0 : $i]:
77.29/10.38	          (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_1])).
77.29/10.38	thf(zip_derived_cl3431, plain,
77.29/10.38	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3428, plain,
77.29/10.38	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3480, plain,
77.29/10.38	    ( (is_of @ sk__2 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')))),
77.29/10.38	    inference('lambda_lifting', [status(thm)],
77.29/10.38	              [zip_derived_cl55, zip_derived_cl3431, zip_derived_cl3428])).
77.29/10.38	thf(zip_derived_cl56, plain,
77.29/10.38	    ( (is_of @ sk__4 @ 
77.29/10.38	       (^[Y0 : $i]:
77.29/10.38	          (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_1])).
77.29/10.38	thf(zip_derived_cl3431, plain,
77.29/10.38	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3428, plain,
77.29/10.38	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3481, plain,
77.29/10.38	    ( (is_of @ sk__4 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')))),
77.29/10.38	    inference('lambda_lifting', [status(thm)],
77.29/10.38	              [zip_derived_cl56, zip_derived_cl3431, zip_derived_cl3428])).
77.29/10.38	thf(zip_derived_cl3, plain,
77.29/10.38	    (![X0 : $i, X1 : $i]:
77.29/10.38	       ($true | ~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ X1))))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_2])).
77.29/10.38	thf(zip_derived_cl1, plain,
77.29/10.38	    (![X0 : $i]:
77.29/10.38	       (((ordsucc @ X0) != (ordsucc @ emptyset))
77.29/10.38	        | ~ (is_of @ X0 @ 
77.29/10.38	             (^[Y0 : $i]:
77.29/10.38	                (in @ Y0 @ 
77.29/10.38	                 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_3])).
77.29/10.38	thf(zip_derived_cl3429, plain,
77.29/10.38	    (![X2 : $i]:
77.29/10.38	       (('#l_lift2064' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift2063')))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl3432, plain,
77.29/10.38	    ((('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')) = ('#l_lift2064'))),
77.29/10.38	    define([status(thm)])).
77.29/10.38	thf(zip_derived_cl58, plain, (~ (n_some @ (diffprop @ sk__2 @ sk__4))),
77.29/10.38	    inference('cnf', [status(esa)], [zf_stmt_1])).
77.29/10.38	thf(def_or3, axiom,(( or3  ) =
77.29/10.38	  (^[X0:$o,X1:$o,X2:$o]: ( l_or @ X0 @ ( l_or @ X1 @ X2 ) )))).
77.29/10.38	thf('24', plain,
77.29/10.38	    (( or3 ) = ( ^[X0:$o,X1:$o,X2:$o]: ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) )),
77.29/10.38	    inference('simplify_rw_rule', [status(thm)], [def_or3, '13', '11', '9'])).
77.29/10.38	thf('25', plain,
77.29/10.39	    (( or3 ) =
77.29/10.39	     ( ^[V_1:$o,V_2:$o,V_3:$o]: ( l_or @ V_1 @ ( l_or @ V_2 @ V_3 ) ) )),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(satz10a, axiom,
77.29/10.39	  (all_of @
77.29/10.39	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
77.29/10.39	   ( ^[X0:$i]:
77.29/10.39	     ( all_of @
77.29/10.39	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
77.29/10.39	       ( ^[X1:$i]:
77.29/10.39	         ( or3 @
77.29/10.39	           ( n_is @ X0 @ X1 ) @ ( d_29_ii @ X0 @ X1 ) @ ( iii @ X0 @ X1 ) ) ) ) ))).
77.29/10.39	thf(zf_stmt_6, axiom,
77.29/10.39	  (![X4:$i]:
77.29/10.39	   ( ( is_of @
77.29/10.39	       X4 @ 
77.29/10.39	       ( ^[V_1:$i]:
77.29/10.39	         ( in @
77.29/10.39	           V_1 @ 
77.29/10.39	           ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.39	     ( ![X6:$i]:
77.29/10.39	       ( ( is_of @
77.29/10.39	           X6 @ 
77.29/10.39	           ( ^[V_3:$i]:
77.29/10.39	             ( in @
77.29/10.39	               V_3 @ 
77.29/10.39	               ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.39	         ( ( ( X4 ) != ( X6 ) ) =>
77.29/10.39	           ( ( ~( n_some @ ( diffprop @ X4 @ X6 ) ) ) => ( iii @ X4 @ X6 ) ) ) ) ) ))).
77.29/10.39	thf(zip_derived_cl54, plain,
77.29/10.39	    (![X0 : $i, X1 : $i]:
77.29/10.39	       (~ (is_of @ X0 @ 
77.29/10.39	           (^[Y0 : $i]:
77.29/10.39	              (in @ Y0 @ 
77.29/10.39	               (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))
77.29/10.39	        |  (n_some @ (diffprop @ X1 @ X0))
77.29/10.39	        |  (iii @ X1 @ X0)
77.29/10.39	        | ((X1) = (X0))
77.29/10.39	        | ~ (is_of @ X1 @ 
77.29/10.39	             (^[Y0 : $i]:
77.29/10.39	                (in @ Y0 @ 
77.29/10.39	                 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))),
77.29/10.39	    inference('cnf', [status(esa)], [zf_stmt_6])).
77.29/10.39	thf(zip_derived_cl3431, plain,
77.29/10.39	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3428, plain,
77.29/10.39	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3431, plain,
77.29/10.39	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3428, plain,
77.29/10.39	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3479, plain,
77.29/10.39	    (![X0 : $i, X1 : $i]:
77.29/10.39	       (~ (is_of @ X0 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')))
77.29/10.39	        |  (n_some @ (diffprop @ X1 @ X0))
77.29/10.39	        |  (iii @ X1 @ X0)
77.29/10.39	        | ((X1) = (X0))
77.29/10.39	        | ~ (is_of @ X1 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063'))))),
77.29/10.39	    inference('lambda_lifting', [status(thm)],
77.29/10.39	              [zip_derived_cl54, zip_derived_cl3431, zip_derived_cl3428, 
77.29/10.39	               zip_derived_cl3431, zip_derived_cl3428])).
77.29/10.39	thf(satz11, axiom,
77.29/10.39	  (all_of @
77.29/10.39	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
77.29/10.39	   ( ^[X0:$i]:
77.29/10.39	     ( all_of @
77.29/10.39	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
77.29/10.39	       ( ^[X1:$i]: ( ( d_29_ii @ X0 @ X1 ) => ( iii @ X1 @ X0 ) ) ) ) ))).
77.29/10.39	thf(zf_stmt_7, axiom,
77.29/10.39	  (![X4:$i]:
77.29/10.39	   ( ( is_of @
77.29/10.39	       X4 @ 
77.29/10.39	       ( ^[V_1:$i]:
77.29/10.39	         ( in @
77.29/10.39	           V_1 @ 
77.29/10.39	           ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.39	     ( ![X6:$i]:
77.29/10.39	       ( ( is_of @
77.29/10.39	           X6 @ 
77.29/10.39	           ( ^[V_3:$i]:
77.29/10.39	             ( in @
77.29/10.39	               V_3 @ 
77.29/10.39	               ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.39	         ( ( n_some @ ( diffprop @ X4 @ X6 ) ) => ( iii @ X6 @ X4 ) ) ) ) ))).
77.29/10.39	thf(zip_derived_cl32, plain,
77.29/10.39	    (![X0 : $i, X1 : $i]:
77.29/10.39	       (~ (is_of @ X0 @ 
77.29/10.39	           (^[Y0 : $i]:
77.29/10.39	              (in @ Y0 @ 
77.29/10.39	               (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))
77.29/10.39	        |  (iii @ X0 @ X1)
77.29/10.39	        | ~ (n_some @ (diffprop @ X1 @ X0))
77.29/10.39	        | ~ (is_of @ X1 @ 
77.29/10.39	             (^[Y0 : $i]:
77.29/10.39	                (in @ Y0 @ 
77.29/10.39	                 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))),
77.29/10.39	    inference('cnf', [status(esa)], [zf_stmt_7])).
77.29/10.39	thf(zip_derived_cl3431, plain,
77.29/10.39	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3428, plain,
77.29/10.39	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3431, plain,
77.29/10.39	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3428, plain,
77.29/10.39	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3456, plain,
77.29/10.39	    (![X0 : $i, X1 : $i]:
77.29/10.39	       (~ (is_of @ X0 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')))
77.29/10.39	        |  (iii @ X0 @ X1)
77.29/10.39	        | ~ (n_some @ (diffprop @ X1 @ X0))
77.29/10.39	        | ~ (is_of @ X1 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063'))))),
77.29/10.39	    inference('lambda_lifting', [status(thm)],
77.29/10.39	              [zip_derived_cl32, zip_derived_cl3431, zip_derived_cl3428, 
77.29/10.39	               zip_derived_cl3431, zip_derived_cl3428])).
77.29/10.39	thf(satz16a, axiom,
77.29/10.39	  (all_of @
77.29/10.39	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
77.29/10.39	   ( ^[X0:$i]:
77.29/10.39	     ( all_of @
77.29/10.39	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
77.29/10.39	       ( ^[X1:$i]:
77.29/10.39	         ( all_of @
77.29/10.39	           ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 
77.29/10.39	           ( ^[X2:$i]:
77.29/10.39	             ( ( lessis @ X0 @ X1 ) =>
77.29/10.39	               ( ( iii @ X1 @ X2 ) => ( iii @ X0 @ X2 ) ) ) ) ) ) ) ))).
77.29/10.39	thf(zf_stmt_8, axiom,
77.29/10.39	  (![X4:$i]:
77.29/10.39	   ( ( is_of @
77.29/10.39	       X4 @ 
77.29/10.39	       ( ^[V_1:$i]:
77.29/10.39	         ( in @
77.29/10.39	           V_1 @ 
77.29/10.39	           ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.39	     ( ![X6:$i]:
77.29/10.39	       ( ( is_of @
77.29/10.39	           X6 @ 
77.29/10.39	           ( ^[V_3:$i]:
77.29/10.39	             ( in @
77.29/10.39	               V_3 @ 
77.29/10.39	               ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.39	         ( ![X8:$i]:
77.29/10.39	           ( ( is_of @
77.29/10.39	               X8 @ 
77.29/10.39	               ( ^[V_5:$i]:
77.29/10.39	                 ( in @
77.29/10.39	                   V_5 @ 
77.29/10.39	                   ( d_Sep @
77.29/10.39	                     omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.39	             ( ( ( ~( iii @ X4 @ X6 ) ) => ( ( X4 ) = ( X6 ) ) ) =>
77.29/10.39	               ( ( iii @ X6 @ X8 ) => ( iii @ X4 @ X8 ) ) ) ) ) ) ) ))).
77.29/10.39	thf(zip_derived_cl48, plain,
77.29/10.39	    (![X0 : $i, X1 : $i, X2 : $i]:
77.29/10.39	       (~ (is_of @ X0 @ 
77.29/10.39	           (^[Y0 : $i]:
77.29/10.39	              (in @ Y0 @ 
77.29/10.39	               (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))
77.29/10.39	        | ~ (iii @ X1 @ X0)
77.29/10.39	        |  (iii @ X1 @ X2)
77.29/10.39	        | ~ (iii @ X0 @ X2)
77.29/10.39	        | ~ (is_of @ X2 @ 
77.29/10.39	             (^[Y0 : $i]:
77.29/10.39	                (in @ Y0 @ 
77.29/10.39	                 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))
77.29/10.39	        | ~ (is_of @ X1 @ 
77.29/10.39	             (^[Y0 : $i]:
77.29/10.39	                (in @ Y0 @ 
77.29/10.39	                 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))),
77.29/10.39	    inference('cnf', [status(esa)], [zf_stmt_8])).
77.29/10.39	thf(zip_derived_cl3431, plain,
77.29/10.39	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3428, plain,
77.29/10.39	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3431, plain,
77.29/10.39	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3428, plain,
77.29/10.39	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3431, plain,
77.29/10.39	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3428, plain,
77.29/10.39	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3473, plain,
77.29/10.39	    (![X0 : $i, X1 : $i, X2 : $i]:
77.29/10.39	       (~ (is_of @ X0 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')))
77.29/10.39	        | ~ (iii @ X1 @ X0)
77.29/10.39	        |  (iii @ X1 @ X2)
77.29/10.39	        | ~ (iii @ X0 @ X2)
77.29/10.39	        | ~ (is_of @ X2 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')))
77.29/10.39	        | ~ (is_of @ X1 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063'))))),
77.29/10.39	    inference('lambda_lifting', [status(thm)],
77.29/10.39	              [zip_derived_cl48, zip_derived_cl3431, zip_derived_cl3428, 
77.29/10.39	               zip_derived_cl3431, zip_derived_cl3428, zip_derived_cl3431, 
77.29/10.39	               zip_derived_cl3428])).
77.29/10.39	thf(satz12, axiom,
77.29/10.39	  (all_of @
77.29/10.39	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
77.29/10.39	   ( ^[X0:$i]:
77.29/10.39	     ( all_of @
77.29/10.39	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
77.29/10.39	       ( ^[X1:$i]: ( ( iii @ X0 @ X1 ) => ( d_29_ii @ X1 @ X0 ) ) ) ) ))).
77.29/10.39	thf(zf_stmt_9, axiom,
77.29/10.39	  (![X4:$i]:
77.29/10.39	   ( ( is_of @
77.29/10.39	       X4 @ 
77.29/10.39	       ( ^[V_1:$i]:
77.29/10.39	         ( in @
77.29/10.39	           V_1 @ 
77.29/10.39	           ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.39	     ( ![X6:$i]:
77.29/10.39	       ( ( is_of @
77.29/10.39	           X6 @ 
77.29/10.39	           ( ^[V_3:$i]:
77.29/10.39	             ( in @
77.29/10.39	               V_3 @ 
77.29/10.39	               ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) =>
77.29/10.39	         ( ( iii @ X4 @ X6 ) => ( n_some @ ( diffprop @ X6 @ X4 ) ) ) ) ) ))).
77.29/10.39	thf(zip_derived_cl26, plain,
77.29/10.39	    (![X0 : $i, X1 : $i]:
77.29/10.39	       (~ (is_of @ X0 @ 
77.29/10.39	           (^[Y0 : $i]:
77.29/10.39	              (in @ Y0 @ 
77.29/10.39	               (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))
77.29/10.39	        |  (n_some @ (diffprop @ X0 @ X1))
77.29/10.39	        | ~ (iii @ X1 @ X0)
77.29/10.39	        | ~ (is_of @ X1 @ 
77.29/10.39	             (^[Y0 : $i]:
77.29/10.39	                (in @ Y0 @ 
77.29/10.39	                 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))),
77.29/10.39	    inference('cnf', [status(esa)], [zf_stmt_9])).
77.29/10.39	thf(zip_derived_cl3431, plain,
77.29/10.39	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3428, plain,
77.29/10.39	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3431, plain,
77.29/10.39	    (![X1 : $i, X2 : $i]: (('#l_lift2065' @ X1 @ X2) = (in @ X2 @ X1))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3428, plain,
77.29/10.39	    (![X1 : $i]: (('#l_lift2063' @ X1) = (((X1) != (emptyset))))),
77.29/10.39	    define([status(thm)])).
77.29/10.39	thf(zip_derived_cl3450, plain,
77.29/10.39	    (![X0 : $i, X1 : $i]:
77.29/10.39	       (~ (is_of @ X0 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063')))
77.29/10.39	        |  (n_some @ (diffprop @ X0 @ X1))
77.29/10.39	        | ~ (iii @ X1 @ X0)
77.29/10.39	        | ~ (is_of @ X1 @ ('#l_lift2065' @ (d_Sep @ omega @ '#l_lift2063'))))),
77.29/10.39	    inference('lambda_lifting', [status(thm)],
77.29/10.39	              [zip_derived_cl26, zip_derived_cl3431, zip_derived_cl3428, 
77.29/10.39	               zip_derived_cl3431, zip_derived_cl3428])).
77.29/10.39	thf(zip_derived_cl3505, plain, ($false),
77.29/10.39	    inference('eprover', [status(thm)],
77.29/10.39	              [zip_derived_cl59, zip_derived_cl57, zip_derived_cl3482, 
77.29/10.39	               zip_derived_cl3477, zip_derived_cl3476, zip_derived_cl3480, 
77.29/10.39	               zip_derived_cl3481, zip_derived_cl3432, zip_derived_cl58, 
77.29/10.39	               zip_derived_cl3479, zip_derived_cl3456, zip_derived_cl3473, 
77.29/10.39	               zip_derived_cl3450])).
77.29/10.39	
77.29/10.39	% SZS output end Refutation
77.29/10.39	
77.29/10.39	
77.29/10.39	% Terminating...
78.07/10.50	% Runner terminated.
78.07/10.52	% Zipperpin 1.5 exiting
78.07/10.52	EOF