0.06/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.14	% Command    : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.pmx9iPoSxn
0.14/0.35	% Computer   : n013.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 960
0.14/0.35	% DateTime   : Thu Jul  2 09:13:19 EDT 2020
0.14/0.35	% CPUTime    : 
0.14/0.35	% Running portfolio for 120 s
0.14/0.35	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.14/0.35	% Number of cores: 8
0.14/0.36	% Python version: Python 3.6.8
0.14/0.36	% Running in HO mode
0.45/0.62	% Estimated wc time : 1286
0.45/0.62	% Estimated cpu time (7 cpus) : 183.71428571428572
0.51/0.73	% /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s
0.51/0.73	% /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s
0.51/0.73	% /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s
0.51/0.73	% /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s
0.51/0.73	% /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s
0.51/0.74	% /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s
0.51/0.74	% /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s
71.44/11.00	% /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s
102.88/15.93	% /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s
103.31/16.13	% /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s
140.62/21.69	% /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s
142.55/22.19	% /export/starexec/sandbox2/solver/bin/lams/b.split.sh running for 31s
179.29/27.80	% /export/starexec/sandbox2/solver/bin/lams/s4.sh running for 15s
181.60/28.23	% /export/starexec/sandbox2/solver/bin/lams/b.rw.sh running for 26s
253.94/38.81	% /export/starexec/sandbox2/solver/bin/lams/c_ic.sh running for 42s
281.63/43.14	% /export/starexec/sandbox2/solver/bin/lams/s1.f.sh running for 15s
283.65/43.55	% /export/starexec/sandbox2/solver/bin/lams/c.preprocess2.sh running for 21s
345.44/53.58	% /export/starexec/sandbox2/solver/bin/lams/sh.or.sh running for 26s
350.38/54.43	% /export/starexec/sandbox2/solver/bin/lams/new.cs3.comb.sh running for 18s
372.09/58.20	% /export/starexec/sandbox2/solver/bin/lams/old_b2.sh running for 31s
383.46/60.16	% /export/starexec/sandbox2/solver/bin/lams/sp5.sh running for 36s
414.89/64.72	% /export/starexec/sandbox2/solver/bin/lams/b2.sh running for 15s
443.33/68.81	% /export/starexec/sandbox2/solver/bin/lams/b.lcnf.od.sh running for 26s
468.96/72.54	% /export/starexec/sandbox2/solver/bin/lams/c.s.sh running for 36s
516.49/79.77	% /export/starexec/sandbox2/solver/bin/lams/b3.sh running for 26s
518.66/80.35	% Solved by lams/c.s.sh.
518.66/80.35	% Running : timeout 27 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.pmx9iPoSxn/e_input632a99 --cpu-limit=25 --auto-schedule -s -p.
518.66/80.35	% done 979 iterations in 7.697s
518.66/80.35	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
518.66/80.35	% SZS output start Refutation
518.66/80.35	tff(def_n_eq, axiom, n_eq() =
518.66/80.35	  ^[X0,X1]: n_is(n_ts(num(X0),den(X1)),n_ts(num(X1),den(X0)))).
518.66/80.35	tff(def_den, axiom, den() = second1(nat)).
518.66/80.35	tff(def_second1, axiom, second1() = ^[X0,X1]: ap(X1,n_2t)).
518.66/80.35	tff('0', plain, second1 = (^[X0,X1]: ap(X1,n_2t)),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_second1])).
518.66/80.35	tff('1', plain, second1 = (^[V_1,V_2]: ap(V_2,n_2t)), define([status(thm)])).
518.66/80.35	tff(def_nat, axiom, nat() = d_Sep(omega,^[X0]: (X0 != emptyset))).
518.66/80.35	tff('2', plain, nat = d_Sep(omega,^[X0]: (X0 != emptyset)),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_nat])).
518.66/80.35	tff('3', plain, nat = d_Sep(omega,^[V_1]: (V_1 != emptyset)),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('4', plain, den = second1(nat),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_den, '1', '3'])).
518.66/80.35	tff('5', plain, den = second1(nat), define([status(thm)])).
518.66/80.35	tff(def_num, axiom, num() = first1(nat)).
518.66/80.35	tff(def_first1, axiom, first1() = ^[X0,X1]: ap(X1,n_1t)).
518.66/80.35	tff(def_n_1t, axiom, n_1t() = outn(n_2,n_1)).
518.66/80.35	tff(def_n_2, axiom, n_2() = n_pl(n_1,n_1)).
518.66/80.35	tff(def_n_1, axiom, n_1() = ordsucc(emptyset)).
518.66/80.35	tff('6', plain, n_1 = ordsucc(emptyset),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_n_1])).
518.66/80.35	tff('7', plain, n_1 = ordsucc(emptyset), define([status(thm)])).
518.66/80.35	tff('8', plain, n_2 = n_pl(n_1,n_1),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_n_2, '7'])).
518.66/80.35	tff('9', plain, n_2 = n_pl(n_1,n_1), define([status(thm)])).
518.66/80.35	tff('10', plain, n_1t = outn(n_2,n_1),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_n_1t, '9', '7'])).
518.66/80.35	tff('11', plain, n_1t = outn(n_2,n_1), define([status(thm)])).
518.66/80.35	tff('12', plain, first1 = (^[X0,X1]: ap(X1,n_1t)),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_first1, '11', '9', '7'])).
518.66/80.35	tff('13', plain, first1 = (^[V_1,V_2]: ap(V_2,n_1t)), define([status(thm)])).
518.66/80.35	tff('14', plain, num = first1(nat),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_num, '13', '11', '3'])).
518.66/80.35	tff('15', plain, num = first1(nat), define([status(thm)])).
518.66/80.35	tff(def_n_ts, axiom, n_ts() = ^[X0]: ap(times(X0))).
518.66/80.35	tff('16', plain, n_ts = (^[X0]: ap(times(X0))),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_n_ts])).
518.66/80.35	tff('17', plain, n_ts = (^[V_1]: ap(times(V_1))), define([status(thm)])).
518.66/80.35	tff(def_n_is, axiom, n_is() = e_is(nat)).
518.66/80.35	tff(def_e_is, axiom, e_is() = ^[X0,X,Y]: (X = Y)).
518.66/80.35	tff('18', plain, e_is = (^[X0,X,Y]: (X = Y)),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_e_is])).
518.66/80.35	tff('19', plain, e_is = (^[V_1,V_2,V_3]: (V_2 = V_3)), define([status(thm)])).
518.66/80.35	tff('20', plain, n_is = e_is(nat),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_n_is, '3', '19'])).
518.66/80.35	tff('21', plain, n_is = e_is(nat), define([status(thm)])).
518.66/80.35	tff('22', plain,
518.66/80.35	    n_eq = (^[X0,X1]: n_is(n_ts(num(X0),den(X1)),n_ts(num(X1),den(X0)))),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)],
518.66/80.35	              [def_n_eq, '5', '15', '1', '13', '11', '9', '17', '7', '21', 
518.66/80.35	               '3', '19'])).
518.66/80.35	tff('23', plain,
518.66/80.35	    n_eq =
518.66/80.35	    (^[V_1,V_2]: n_is(n_ts(num(V_1),den(V_2)),n_ts(num(V_2),den(V_1)))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff(def_n_fr, axiom, n_fr() = pair1(nat)).
518.66/80.35	tff(def_pair1, axiom, pair1() =
518.66/80.35	  ^[X0,X1,X2]:
518.66/80.35	    d_Sigma(d_1to(n_2),^[X3]: ite(e_is(d_1to(n_2),X3,n_1t),X0,X1,X2))).
518.66/80.35	tff(def_d_1to, axiom, d_1to() = ^[X0]: d_Sep(nat,^[X1]: lessis(X1,X0))).
518.66/80.35	tff('24', plain, d_1to = (^[X0]: d_Sep(nat,^[X1]: lessis(X1,X0))),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_d_1to, '3'])).
518.66/80.35	tff('25', plain, d_1to = (^[V_1]: d_Sep(nat,^[V_2]: lessis(V_2,V_1))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff(def_ite, axiom, ite() = ^[X0:$o,X1,X2,X3]: ind(X1,prop1(X0,X1,X2,X3))).
518.66/80.35	tff('26', plain, ite = (^[X0:$o,X1,X2,X3]: ind(X1,prop1(X0,X1,X2,X3))),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_ite])).
518.66/80.35	tff('27', plain,
518.66/80.35	    ite = (^[V_1:$o,V_2,V_3,V_4]: ind(V_2,prop1(V_1,V_2,V_3,V_4))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('28', plain,
518.66/80.35	    pair1 =
518.66/80.35	    (^[X0,X1,X2]:
518.66/80.35	       d_Sigma(d_1to(n_2),^[X3]: ite(e_is(d_1to(n_2),X3,n_1t),X0,X1,X2))),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)],
518.66/80.35	              [def_pair1, '11', '9', '25', '7', '3', '27', '19'])).
518.66/80.35	tff('29', plain,
518.66/80.35	    pair1 =
518.66/80.35	    (^[V_1,V_2,V_3]:
518.66/80.35	       d_Sigma(d_1to(n_2),^[V_4]: ite(e_is(d_1to(n_2),V_4,n_1t),V_1,V_2,V_3))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('30', plain, n_fr = pair1(nat),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)],
518.66/80.35	              [def_n_fr, '29', '11', '9', '25', '7', '3', '27', '19'])).
518.66/80.35	tff('31', plain, n_fr = pair1(nat), define([status(thm)])).
518.66/80.35	tff(def_all_of, axiom, all_of() =
518.66/80.35	  ^[X0:(($i > $o)),X1:(($i > $o))]: (![X2]: (is_of(X2,X0) => X1(X2)))).
518.66/80.35	tff('32', plain,
518.66/80.35	    all_of =
518.66/80.35	    (^[X0:(($i > $o)),X1:(($i > $o))]: (![X2]: (is_of(X2,X0) => X1(X2)))),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_all_of])).
518.66/80.35	tff('33', plain,
518.66/80.35	    all_of =
518.66/80.35	    (^[V_1:(($i > $o)),V_2:(($i > $o))]: (![X4]: (is_of(X4,V_1) => V_2(X4)))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff(satz40c, conjecture,
518.66/80.35	  (all_of(^[X0]: in(X0,nat),
518.66/80.35	          ^[X0]:
518.66/80.35	            all_of(^[X1]: in(X1,nat),
518.66/80.35	                   ^[X1]:
518.66/80.35	                     all_of(^[X2]: in(X2,nat),
518.66/80.35	                            ^[X2]:
518.66/80.35	                              n_eq(n_fr(n_ts(X0,X2),n_ts(X1,X2)),n_fr(X0,X1))))))).
518.66/80.35	tff(zf_stmt_0, conjecture,
518.66/80.35	  (![X4]:
518.66/80.35	     (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
518.66/80.35	      (![X6]:
518.66/80.35	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
518.66/80.35	          (![X8]:
518.66/80.35	             (is_of(X8,^[V_5]: in(V_5,d_Sep(omega,^[V_6]: (V_6 != emptyset)))) =>
518.66/80.35	              (ap(times(ap(d_Sigma(d_Sep(d_Sep(omega,
518.66/80.35	                                               ^[V_7]: (V_7 != emptyset)),
518.66/80.35	                                         ^[V_8]:
518.66/80.35	                                           lessis(V_8,
518.66/80.35	                                                  n_pl(ordsucc(emptyset),
518.66/80.35	                                                       ordsucc(emptyset)))),
518.66/80.35	                                   ^[V_9]:
518.66/80.35	                                     ind(d_Sep(omega,
518.66/80.35	                                               ^[V_10]: (V_10 != emptyset)),
518.66/80.35	                                         prop1(V_9 =
518.66/80.35	                                               outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                         ordsucc(emptyset)),
518.66/80.35	                                                    ordsucc(emptyset)),
518.66/80.35	                                               d_Sep(omega,
518.66/80.35	                                                     ^[V_11]:
518.66/80.35	                                                       (V_11 != emptyset)),
518.66/80.35	                                               ap(times(X4),X8),
518.66/80.35	                                               ap(times(X6),X8)))),
518.66/80.35	                           outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
518.66/80.35	                                ordsucc(emptyset)))),
518.66/80.35	                  ap(d_Sigma(d_Sep(d_Sep(omega,^[V_12]: (V_12 != emptyset)),
518.66/80.35	                                   ^[V_13]:
518.66/80.35	                                     lessis(V_13,
518.66/80.35	                                            n_pl(ordsucc(emptyset),
518.66/80.35	                                                 ordsucc(emptyset)))),
518.66/80.35	                             ^[V_14]:
518.66/80.35	                               ind(d_Sep(omega,^[V_15]: (V_15 != emptyset)),
518.66/80.35	                                   prop1(V_14 =
518.66/80.35	                                         outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                   ordsucc(emptyset)),
518.66/80.35	                                              ordsucc(emptyset)),
518.66/80.35	                                         d_Sep(omega,
518.66/80.35	                                               ^[V_16]: (V_16 != emptyset)),
518.66/80.35	                                         X4,X6))),
518.66/80.35	                     n_2t)) =
518.66/80.35	               ap(times(ap(d_Sigma(d_Sep(d_Sep(omega,
518.66/80.35	                                               ^[V_17]: (V_17 != emptyset)),
518.66/80.35	                                         ^[V_18]:
518.66/80.35	                                           lessis(V_18,
518.66/80.35	                                                  n_pl(ordsucc(emptyset),
518.66/80.35	                                                       ordsucc(emptyset)))),
518.66/80.35	                                   ^[V_19]:
518.66/80.35	                                     ind(d_Sep(omega,
518.66/80.35	                                               ^[V_20]: (V_20 != emptyset)),
518.66/80.35	                                         prop1(V_19 =
518.66/80.35	                                               outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                         ordsucc(emptyset)),
518.66/80.35	                                                    ordsucc(emptyset)),
518.66/80.35	                                               d_Sep(omega,
518.66/80.35	                                                     ^[V_21]:
518.66/80.35	                                                       (V_21 != emptyset)),
518.66/80.35	                                               X4,X6))),
518.66/80.35	                           outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
518.66/80.35	                                ordsucc(emptyset)))),
518.66/80.35	                  ap(d_Sigma(d_Sep(d_Sep(omega,^[V_22]: (V_22 != emptyset)),
518.66/80.35	                                   ^[V_23]:
518.66/80.35	                                     lessis(V_23,
518.66/80.35	                                            n_pl(ordsucc(emptyset),
518.66/80.35	                                                 ordsucc(emptyset)))),
518.66/80.35	                             ^[V_24]:
518.66/80.35	                               ind(d_Sep(omega,^[V_25]: (V_25 != emptyset)),
518.66/80.35	                                   prop1(V_24 =
518.66/80.35	                                         outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                   ordsucc(emptyset)),
518.66/80.35	                                              ordsucc(emptyset)),
518.66/80.35	                                         d_Sep(omega,
518.66/80.35	                                               ^[V_26]: (V_26 != emptyset)),
518.66/80.35	                                         ap(times(X4),X8),ap(times(X6),X8)))),
518.66/80.35	                     n_2t)))))))))).
518.66/80.35	tff(zf_stmt_1, negated_conjecture,
518.66/80.35	  (~
518.66/80.35	    (![X4]:
518.66/80.35	       (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
518.66/80.35	        (![X6]:
518.66/80.35	           (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
518.66/80.35	            (![X8]:
518.66/80.35	               (is_of(X8,
518.66/80.35	                      ^[V_5]: in(V_5,d_Sep(omega,^[V_6]: (V_6 != emptyset)))) =>
518.66/80.35	                (ap(times(ap(d_Sigma(d_Sep(d_Sep(omega,
518.66/80.35	                                                 ^[V_7]: (V_7 != emptyset)),
518.66/80.35	                                           ^[V_8]:
518.66/80.35	                                             lessis(V_8,
518.66/80.35	                                                    n_pl(ordsucc(emptyset),
518.66/80.35	                                                         ordsucc(emptyset)))),
518.66/80.35	                                     ^[V_9]:
518.66/80.35	                                       ind(d_Sep(omega,
518.66/80.35	                                                 ^[V_10]: (V_10 != emptyset)),
518.66/80.35	                                           prop1(V_9 =
518.66/80.35	                                                 outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                           ordsucc(emptyset)),
518.66/80.35	                                                      ordsucc(emptyset)),
518.66/80.35	                                                 d_Sep(omega,
518.66/80.35	                                                       ^[V_11]:
518.66/80.35	                                                         (V_11 != emptyset)),
518.66/80.35	                                                 ap(times(X4),X8),
518.66/80.35	                                                 ap(times(X6),X8)))),
518.66/80.35	                             outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
518.66/80.35	                                  ordsucc(emptyset)))),
518.66/80.35	                    ap(d_Sigma(d_Sep(d_Sep(omega,^[V_12]: (V_12 != emptyset)),
518.66/80.35	                                     ^[V_13]:
518.66/80.35	                                       lessis(V_13,
518.66/80.35	                                              n_pl(ordsucc(emptyset),
518.66/80.35	                                                   ordsucc(emptyset)))),
518.66/80.35	                               ^[V_14]:
518.66/80.35	                                 ind(d_Sep(omega,^[V_15]: (V_15 != emptyset)),
518.66/80.35	                                     prop1(V_14 =
518.66/80.35	                                           outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                     ordsucc(emptyset)),
518.66/80.35	                                                ordsucc(emptyset)),
518.66/80.35	                                           d_Sep(omega,
518.66/80.35	                                                 ^[V_16]: (V_16 != emptyset)),
518.66/80.35	                                           X4,X6))),
518.66/80.35	                       n_2t)) =
518.66/80.35	                 ap(times(ap(d_Sigma(d_Sep(d_Sep(omega,
518.66/80.35	                                                 ^[V_17]: (V_17 != emptyset)),
518.66/80.35	                                           ^[V_18]:
518.66/80.35	                                             lessis(V_18,
518.66/80.35	                                                    n_pl(ordsucc(emptyset),
518.66/80.35	                                                         ordsucc(emptyset)))),
518.66/80.35	                                     ^[V_19]:
518.66/80.35	                                       ind(d_Sep(omega,
518.66/80.35	                                                 ^[V_20]: (V_20 != emptyset)),
518.66/80.35	                                           prop1(V_19 =
518.66/80.35	                                                 outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                           ordsucc(emptyset)),
518.66/80.35	                                                      ordsucc(emptyset)),
518.66/80.35	                                                 d_Sep(omega,
518.66/80.35	                                                       ^[V_21]:
518.66/80.35	                                                         (V_21 != emptyset)),
518.66/80.35	                                                 X4,X6))),
518.66/80.35	                             outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
518.66/80.35	                                  ordsucc(emptyset)))),
518.66/80.35	                    ap(d_Sigma(d_Sep(d_Sep(omega,^[V_22]: (V_22 != emptyset)),
518.66/80.35	                                     ^[V_23]:
518.66/80.35	                                       lessis(V_23,
518.66/80.35	                                              n_pl(ordsucc(emptyset),
518.66/80.35	                                                   ordsucc(emptyset)))),
518.66/80.35	                               ^[V_24]:
518.66/80.35	                                 ind(d_Sep(omega,^[V_25]: (V_25 != emptyset)),
518.66/80.35	                                     prop1(V_24 =
518.66/80.35	                                           outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                     ordsucc(emptyset)),
518.66/80.35	                                                ordsucc(emptyset)),
518.66/80.35	                                           d_Sep(omega,
518.66/80.35	                                                 ^[V_26]: (V_26 != emptyset)),
518.66/80.35	                                           ap(times(X4),X8),ap(times(X6),X8)))),
518.66/80.35	                       n_2t))))))))))).
518.66/80.35	tff('34', plain,
518.66/80.35	     is_of(sk_X6, 
518.66/80.35	       (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))),
518.66/80.35	    inference('cnf', [status(esa)], [zf_stmt_1])).
518.66/80.35	tff(e_fisi, axiom,
518.66/80.35	  (![X0,X1]:
518.66/80.35	     all_of(^[X2]: in(X2,d_Pi(X0,^[X3]: X1)),
518.66/80.35	            ^[X2]:
518.66/80.35	              all_of(^[X3]: in(X3,d_Pi(X0,^[X4]: X1)),
518.66/80.35	                     ^[X3]:
518.66/80.35	                       (all_of(^[X4]: in(X4,X0),
518.66/80.35	                               ^[X4]: e_is(X1,ap(X2,X4),ap(X3,X4))) =>
518.66/80.35	                        e_is(d_Pi(X0,^[X4]: X1),X2,X3)))))).
518.66/80.35	tff(zf_stmt_2, axiom,
518.66/80.35	  (![X4,X6,X8]:
518.66/80.35	     (is_of(X8,^[V_1]: in(V_1,d_Pi(X4,^[V_2]: X6))) =>
518.66/80.35	      (![X10]:
518.66/80.35	         (is_of(X10,^[V_3]: in(V_3,d_Pi(X4,^[V_4]: X6))) =>
518.66/80.35	          ((![X12]:
518.66/80.35	              (is_of(X12,^[V_5]: in(V_5,X4)) => (ap(X8,X12) = ap(X10,X12)))) =>
518.66/80.35	           (X8 = X10))))))).
518.66/80.35	tff('35', plain,
518.66/80.35	    ![X23, X24, X25, X26]:
518.66/80.35	      (~ is_of(X23, (^[Y0 : $i]: in(Y0, d_Pi(X24, (^[Y1 : $i]: X25)))))
518.66/80.35	       | X26 = X23
518.66/80.35	       |  is_of(sk_X12(X23, X26, X24), (^[Y0 : $i]: in(Y0, X24)))
518.66/80.35	       | ~ is_of(X26, (^[Y0 : $i]: in(Y0, d_Pi(X24, (^[Y1 : $i]: X25)))))),
518.66/80.35	    inference('cnf', [status(esa)], [zf_stmt_2])).
518.66/80.35	tff('36', plain, ![X24, X27]: '#l_lift36444'(X24, X27) = in(X27, X24),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff(def_d_not, axiom, d_not() = ^[X0:$o]: imp(X0,$false)).
518.66/80.35	tff('37', plain, d_not = (^[X0:$o]: imp(X0,$false)),
518.66/80.35	    inference('simplify_rw_rule', [status(thm)], [def_d_not])).
518.66/80.35	tff('38', plain, d_not = (^[V_1:$o]: imp(V_1,$false)), define([status(thm)])).
518.66/80.35	tff(satz10j, axiom,
518.66/80.35	  (all_of(^[X0]: in(X0,nat),
518.66/80.35	          ^[X0]:
518.66/80.35	            all_of(^[X1]: in(X1,nat),
518.66/80.35	                   ^[X1]: (d_not(moreis(X0,X1)) => iii(X0,X1)))))).
518.66/80.35	tff(zf_stmt_3, axiom,
518.66/80.35	  (![X4]:
518.66/80.35	     (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
518.66/80.35	      (![X6]:
518.66/80.35	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
518.66/80.35	          (imp(moreis(X4,X6),$false) => iii(X4,X6))))))).
518.66/80.35	tff('39', plain,
518.66/80.35	    ![X70, X71]:
518.66/80.35	      (~ is_of(X70, 
518.66/80.35	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
518.66/80.35	       |  iii(X71, X70)
518.66/80.35	       | ~ imp(moreis(X71, X70), $false)
518.66/80.35	       | ~ is_of(X71, 
518.66/80.35	             (^[Y0 : $i]:
518.66/80.35	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
518.66/80.35	    inference('cnf', [status(esa)], [zf_stmt_3])).
518.66/80.35	tff('40', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('41', plain,  is_of(sk_X6, '#l_lift36444'(d_Sep(omega, '#l_lift36445'))),
518.66/80.35	    inference('lambda_lifting', [status(thm)], ['34', '36', '40'])).
518.66/80.35	tff('42', plain,
518.66/80.35	     is_of(sk_X4, 
518.66/80.35	       (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))),
518.66/80.35	    inference('cnf', [status(esa)], [zf_stmt_1])).
518.66/80.35	tff('43', plain, ![X24, X27]: '#l_lift36444'(X24, X27) = in(X27, X24),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('44', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('45', plain,  is_of(sk_X4, '#l_lift36444'(d_Sep(omega, '#l_lift36445'))),
518.66/80.35	    inference('lambda_lifting', [status(thm)], ['42', '43', '44'])).
518.66/80.35	tff('46', plain,
518.66/80.35	     is_of(sk_X8, 
518.66/80.35	       (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))),
518.66/80.35	    inference('cnf', [status(esa)], [zf_stmt_1])).
518.66/80.35	tff('47', plain, ![X24, X27]: '#l_lift36444'(X24, X27) = in(X27, X24),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('48', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('49', plain,  is_of(sk_X8, '#l_lift36444'(d_Sep(omega, '#l_lift36445'))),
518.66/80.35	    inference('lambda_lifting', [status(thm)], ['46', '47', '48'])).
518.66/80.35	tff('50', plain,
518.66/80.35	    ap(
518.66/80.35	      times(
518.66/80.35	        ap(
518.66/80.35	          d_Sigma(
518.66/80.35	            d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	              (^[Y0 : $i]:
518.66/80.35	                 lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	            (^[Y0 : $i]:
518.66/80.35	               ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                 prop1(
518.66/80.35	                   (Y0 =
518.66/80.35	                    outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                      ordsucc(emptyset))), 
518.66/80.35	                   d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                   ap(times(sk_X4), sk_X8), ap(times(sk_X6), sk_X8))))), 
518.66/80.35	          outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), ordsucc(emptyset)))), 
518.66/80.35	      ap(
518.66/80.35	        d_Sigma(
518.66/80.35	          d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	            (^[Y0 : $i]:
518.66/80.35	               lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	          (^[Y0 : $i]:
518.66/80.35	             ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	               prop1(
518.66/80.35	                 (Y0 =
518.66/80.35	                  outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                    ordsucc(emptyset))), 
518.66/80.35	                 d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), sk_X4, sk_X6)))), 
518.66/80.35	        n_2t))
518.66/80.35	     != ap(
518.66/80.35	          times(
518.66/80.35	            ap(
518.66/80.35	              d_Sigma(
518.66/80.35	                d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                  (^[Y0 : $i]:
518.66/80.35	                     lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	                (^[Y0 : $i]:
518.66/80.35	                   ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                     prop1(
518.66/80.35	                       (Y0 =
518.66/80.35	                        outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                          ordsucc(emptyset))), 
518.66/80.35	                       d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), sk_X4, 
518.66/80.35	                       sk_X6)))), 
518.66/80.35	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                ordsucc(emptyset)))), 
518.66/80.35	          ap(
518.66/80.35	            d_Sigma(
518.66/80.35	              d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                (^[Y0 : $i]:
518.66/80.35	                   lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	              (^[Y0 : $i]:
518.66/80.35	                 ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                   prop1(
518.66/80.35	                     (Y0 =
518.66/80.35	                      outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                        ordsucc(emptyset))), 
518.66/80.35	                     d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                     ap(times(sk_X4), sk_X8), ap(times(sk_X6), sk_X8))))), 
518.66/80.35	            n_2t)),
518.66/80.35	    inference('cnf', [status(esa)], [zf_stmt_1])).
518.66/80.35	tff('51', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff(satz40b, axiom,
518.66/80.35	  (all_of(^[X0]: in(X0,nat),
518.66/80.35	          ^[X0]:
518.66/80.35	            all_of(^[X1]: in(X1,nat),
518.66/80.35	                   ^[X1]:
518.66/80.35	                     all_of(^[X2]: in(X2,nat),
518.66/80.35	                            ^[X2]:
518.66/80.35	                              n_eq(n_fr(X0,X1),n_fr(n_ts(X0,X2),n_ts(X1,X2)))))))).
518.66/80.35	tff(zf_stmt_4, axiom,
518.66/80.35	  (![X4]:
518.66/80.35	     (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
518.66/80.35	      (![X6]:
518.66/80.35	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
518.66/80.35	          (![X8]:
518.66/80.35	             (is_of(X8,^[V_5]: in(V_5,d_Sep(omega,^[V_6]: (V_6 != emptyset)))) =>
518.66/80.35	              (ap(times(ap(d_Sigma(d_Sep(d_Sep(omega,
518.66/80.35	                                               ^[V_7]: (V_7 != emptyset)),
518.66/80.35	                                         ^[V_8]:
518.66/80.35	                                           lessis(V_8,
518.66/80.35	                                                  n_pl(ordsucc(emptyset),
518.66/80.35	                                                       ordsucc(emptyset)))),
518.66/80.35	                                   ^[V_9]:
518.66/80.35	                                     ind(d_Sep(omega,
518.66/80.35	                                               ^[V_10]: (V_10 != emptyset)),
518.66/80.35	                                         prop1(V_9 =
518.66/80.35	                                               outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                         ordsucc(emptyset)),
518.66/80.35	                                                    ordsucc(emptyset)),
518.66/80.35	                                               d_Sep(omega,
518.66/80.35	                                                     ^[V_11]:
518.66/80.35	                                                       (V_11 != emptyset)),
518.66/80.35	                                               X4,X6))),
518.66/80.35	                           outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
518.66/80.35	                                ordsucc(emptyset)))),
518.66/80.35	                  ap(d_Sigma(d_Sep(d_Sep(omega,^[V_12]: (V_12 != emptyset)),
518.66/80.35	                                   ^[V_13]:
518.66/80.35	                                     lessis(V_13,
518.66/80.35	                                            n_pl(ordsucc(emptyset),
518.66/80.35	                                                 ordsucc(emptyset)))),
518.66/80.35	                             ^[V_14]:
518.66/80.35	                               ind(d_Sep(omega,^[V_15]: (V_15 != emptyset)),
518.66/80.35	                                   prop1(V_14 =
518.66/80.35	                                         outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                   ordsucc(emptyset)),
518.66/80.35	                                              ordsucc(emptyset)),
518.66/80.35	                                         d_Sep(omega,
518.66/80.35	                                               ^[V_16]: (V_16 != emptyset)),
518.66/80.35	                                         ap(times(X4),X8),ap(times(X6),X8)))),
518.66/80.35	                     n_2t)) =
518.66/80.35	               ap(times(ap(d_Sigma(d_Sep(d_Sep(omega,
518.66/80.35	                                               ^[V_17]: (V_17 != emptyset)),
518.66/80.35	                                         ^[V_18]:
518.66/80.35	                                           lessis(V_18,
518.66/80.35	                                                  n_pl(ordsucc(emptyset),
518.66/80.35	                                                       ordsucc(emptyset)))),
518.66/80.35	                                   ^[V_19]:
518.66/80.35	                                     ind(d_Sep(omega,
518.66/80.35	                                               ^[V_20]: (V_20 != emptyset)),
518.66/80.35	                                         prop1(V_19 =
518.66/80.35	                                               outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                         ordsucc(emptyset)),
518.66/80.35	                                                    ordsucc(emptyset)),
518.66/80.35	                                               d_Sep(omega,
518.66/80.35	                                                     ^[V_21]:
518.66/80.35	                                                       (V_21 != emptyset)),
518.66/80.35	                                               ap(times(X4),X8),
518.66/80.35	                                               ap(times(X6),X8)))),
518.66/80.35	                           outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
518.66/80.35	                                ordsucc(emptyset)))),
518.66/80.35	                  ap(d_Sigma(d_Sep(d_Sep(omega,^[V_22]: (V_22 != emptyset)),
518.66/80.35	                                   ^[V_23]:
518.66/80.35	                                     lessis(V_23,
518.66/80.35	                                            n_pl(ordsucc(emptyset),
518.66/80.35	                                                 ordsucc(emptyset)))),
518.66/80.35	                             ^[V_24]:
518.66/80.35	                               ind(d_Sep(omega,^[V_25]: (V_25 != emptyset)),
518.66/80.35	                                   prop1(V_24 =
518.66/80.35	                                         outn(n_pl(ordsucc(emptyset),
518.66/80.35	                                                   ordsucc(emptyset)),
518.66/80.35	                                              ordsucc(emptyset)),
518.66/80.35	                                         d_Sep(omega,
518.66/80.35	                                               ^[V_26]: (V_26 != emptyset)),
518.66/80.35	                                         X4,X6))),
518.66/80.35	                     n_2t)))))))))).
518.66/80.35	tff('52', plain,
518.66/80.35	    ![X97, X98, X99]:
518.66/80.35	      (~ is_of(X97, 
518.66/80.35	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
518.66/80.35	       | ap(
518.66/80.35	           times(
518.66/80.35	             ap(
518.66/80.35	               d_Sigma(
518.66/80.35	                 d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                   (^[Y0 : $i]:
518.66/80.35	                      lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	                 (^[Y0 : $i]:
518.66/80.35	                    ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                      prop1(
518.66/80.35	                        (Y0 =
518.66/80.35	                         outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                           ordsucc(emptyset))), 
518.66/80.35	                        d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), X98, 
518.66/80.35	                        X97)))), 
518.66/80.35	               outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                 ordsucc(emptyset)))), 
518.66/80.35	           ap(
518.66/80.35	             d_Sigma(
518.66/80.35	               d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                 (^[Y0 : $i]:
518.66/80.35	                    lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	               (^[Y0 : $i]:
518.66/80.35	                  ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                    prop1(
518.66/80.35	                      (Y0 =
518.66/80.35	                       outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                         ordsucc(emptyset))), 
518.66/80.35	                      d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                      ap(times(X98), X99), ap(times(X97), X99))))), n_2t))
518.66/80.35	          = ap(
518.66/80.35	              times(
518.66/80.35	                ap(
518.66/80.35	                  d_Sigma(
518.66/80.35	                    d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                      (^[Y0 : $i]:
518.66/80.35	                         lessis(Y0, 
518.66/80.35	                           n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	                    (^[Y0 : $i]:
518.66/80.35	                       ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                         prop1(
518.66/80.35	                           (Y0 =
518.66/80.35	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                              ordsucc(emptyset))), 
518.66/80.35	                           d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                           ap(times(X98), X99), ap(times(X97), X99))))), 
518.66/80.35	                  outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                    ordsucc(emptyset)))), 
518.66/80.35	              ap(
518.66/80.35	                d_Sigma(
518.66/80.35	                  d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                    (^[Y0 : $i]:
518.66/80.35	                       lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	                  (^[Y0 : $i]:
518.66/80.35	                     ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                       prop1(
518.66/80.35	                         (Y0 =
518.66/80.35	                          outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                            ordsucc(emptyset))), 
518.66/80.35	                         d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), X98, 
518.66/80.35	                         X97)))), n_2t))
518.66/80.35	       | ~ is_of(X99, 
518.66/80.35	             (^[Y0 : $i]:
518.66/80.35	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
518.66/80.35	       | ~ is_of(X98, 
518.66/80.35	             (^[Y0 : $i]:
518.66/80.35	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
518.66/80.35	    inference('cnf', [status(esa)], [zf_stmt_4])).
518.66/80.35	tff('53', plain,
518.66/80.35	    ![X100]:
518.66/80.35	      '#l_lift36446'(X100)
518.66/80.35	       = lessis(X100, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('54', plain,
518.66/80.35	    ![X97, X98, X99]:
518.66/80.35	      (~ is_of(X97, 
518.66/80.35	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
518.66/80.35	       | ap(
518.66/80.35	           times(
518.66/80.35	             ap(
518.66/80.35	               d_Sigma(
518.66/80.35	                 d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                   (^[Y0 : $i]:
518.66/80.35	                      lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	                 (^[Y0 : $i]:
518.66/80.35	                    ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                      prop1(
518.66/80.35	                        (Y0 =
518.66/80.35	                         outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                           ordsucc(emptyset))), 
518.66/80.35	                        d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), X98, 
518.66/80.35	                        X97)))), 
518.66/80.35	               outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                 ordsucc(emptyset)))), 
518.66/80.35	           ap(
518.66/80.35	             d_Sigma(
518.66/80.35	               d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                 (^[Y0 : $i]:
518.66/80.35	                    lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	               (^[Y0 : $i]:
518.66/80.35	                  ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                    prop1(
518.66/80.35	                      (Y0 =
518.66/80.35	                       outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                         ordsucc(emptyset))), 
518.66/80.35	                      d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                      ap(times(X98), X99), ap(times(X97), X99))))), n_2t))
518.66/80.35	          = ap(
518.66/80.35	              times(
518.66/80.35	                ap(
518.66/80.35	                  d_Sigma(
518.66/80.35	                    d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                      (^[Y0 : $i]:
518.66/80.35	                         lessis(Y0, 
518.66/80.35	                           n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	                    (^[Y0 : $i]:
518.66/80.35	                       ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                         prop1(
518.66/80.35	                           (Y0 =
518.66/80.35	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                              ordsucc(emptyset))), 
518.66/80.35	                           d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                           ap(times(X98), X99), ap(times(X97), X99))))), 
518.66/80.35	                  outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                    ordsucc(emptyset)))), 
518.66/80.35	              ap(
518.66/80.35	                d_Sigma(
518.66/80.35	                  d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                    (^[Y0 : $i]:
518.66/80.35	                       lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	                  (^[Y0 : $i]:
518.66/80.35	                     ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                       prop1(
518.66/80.35	                         (Y0 =
518.66/80.35	                          outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                            ordsucc(emptyset))), 
518.66/80.35	                         d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), X98, 
518.66/80.35	                         X97)))), n_2t))
518.66/80.35	       | ~ is_of(X99, 
518.66/80.35	             (^[Y0 : $i]:
518.66/80.35	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
518.66/80.35	       | ~ is_of(X98, 
518.66/80.35	             (^[Y0 : $i]:
518.66/80.35	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
518.66/80.35	    inference('cnf', [status(esa)], [zf_stmt_4])).
518.66/80.35	tff('55', plain,
518.66/80.35	    ![X97, X98, X101]:
518.66/80.35	      '#l_lift36447'(X97, X98, X101)
518.66/80.35	       = ind(d_Sep(omega, '#l_lift36445'), 
518.66/80.35	           prop1(
518.66/80.35	             (X101 =
518.66/80.35	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                ordsucc(emptyset))), d_Sep(omega, '#l_lift36445'), X98, X97)),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('56', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('57', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('58', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('59', plain,
518.66/80.35	    ![X100]:
518.66/80.35	      '#l_lift36446'(X100)
518.66/80.35	       = lessis(X100, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('60', plain,
518.66/80.35	    ![X97, X98, X101]:
518.66/80.35	      '#l_lift36447'(X97, X98, X101)
518.66/80.35	       = ind(d_Sep(omega, '#l_lift36445'), 
518.66/80.35	           prop1(
518.66/80.35	             (X101 =
518.66/80.35	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                ordsucc(emptyset))), d_Sep(omega, '#l_lift36445'), X98, X97)),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('61', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('62', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('63', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('64', plain,
518.66/80.35	    ![X100]:
518.66/80.35	      '#l_lift36446'(X100)
518.66/80.35	       = lessis(X100, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('65', plain,
518.66/80.35	    ![X97, X98, X101]:
518.66/80.35	      '#l_lift36447'(X97, X98, X101)
518.66/80.35	       = ind(d_Sep(omega, '#l_lift36445'), 
518.66/80.35	           prop1(
518.66/80.35	             (X101 =
518.66/80.35	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                ordsucc(emptyset))), d_Sep(omega, '#l_lift36445'), X98, X97)),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('66', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('67', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('68', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('69', plain,
518.66/80.35	    ![X100]:
518.66/80.35	      '#l_lift36446'(X100)
518.66/80.35	       = lessis(X100, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('70', plain,
518.66/80.35	    ![X97, X98, X101]:
518.66/80.35	      '#l_lift36447'(X97, X98, X101)
518.66/80.35	       = ind(d_Sep(omega, '#l_lift36445'), 
518.66/80.35	           prop1(
518.66/80.35	             (X101 =
518.66/80.35	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                ordsucc(emptyset))), d_Sep(omega, '#l_lift36445'), X98, X97)),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('71', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('72', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('73', plain,
518.66/80.35	    ap(
518.66/80.35	      times(
518.66/80.35	        ap(
518.66/80.35	          d_Sigma(d_Sep(d_Sep(omega, '#l_lift36445'), '#l_lift36446'), 
518.66/80.35	            '#l_lift36447'(ap(times(sk_X6), sk_X8), ap(times(sk_X4), sk_X8))), 
518.66/80.35	          outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), ordsucc(emptyset)))), 
518.66/80.35	      ap(
518.66/80.35	        d_Sigma(d_Sep(d_Sep(omega, '#l_lift36445'), '#l_lift36446'), 
518.66/80.35	          '#l_lift36447'(sk_X6, sk_X4)), n_2t))
518.66/80.35	     != ap(
518.66/80.35	          times(
518.66/80.35	            ap(
518.66/80.35	              d_Sigma(d_Sep(d_Sep(omega, '#l_lift36445'), '#l_lift36446'), 
518.66/80.35	                '#l_lift36447'(sk_X6, sk_X4)), 
518.66/80.35	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                ordsucc(emptyset)))), 
518.66/80.35	          ap(
518.66/80.35	            d_Sigma(d_Sep(d_Sep(omega, '#l_lift36445'), '#l_lift36446'), 
518.66/80.35	              '#l_lift36447'(ap(times(sk_X6), sk_X8), 
518.66/80.35	                ap(times(sk_X4), sk_X8))), n_2t)),
518.66/80.35	    inference('lambda_lifting', [status(thm)],
518.66/80.35	              ['50', '51', '53', '55', '56', '57', '58', '59', '60', '61', 
518.66/80.35	               '62', '63', '64', '65', '66', '67', '68', '69', '70', '71', 
518.66/80.35	               '72'])).
518.66/80.35	tff('74', plain,
518.66/80.35	    ![X97, X98, X99]:
518.66/80.35	      (~ is_of(X97, 
518.66/80.35	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
518.66/80.35	       | ap(
518.66/80.35	           times(
518.66/80.35	             ap(
518.66/80.35	               d_Sigma(
518.66/80.35	                 d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                   (^[Y0 : $i]:
518.66/80.35	                      lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	                 (^[Y0 : $i]:
518.66/80.35	                    ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                      prop1(
518.66/80.35	                        (Y0 =
518.66/80.35	                         outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                           ordsucc(emptyset))), 
518.66/80.35	                        d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), X98, 
518.66/80.35	                        X97)))), 
518.66/80.35	               outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                 ordsucc(emptyset)))), 
518.66/80.35	           ap(
518.66/80.35	             d_Sigma(
518.66/80.35	               d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                 (^[Y0 : $i]:
518.66/80.35	                    lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	               (^[Y0 : $i]:
518.66/80.35	                  ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                    prop1(
518.66/80.35	                      (Y0 =
518.66/80.35	                       outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                         ordsucc(emptyset))), 
518.66/80.35	                      d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                      ap(times(X98), X99), ap(times(X97), X99))))), n_2t))
518.66/80.35	          = ap(
518.66/80.35	              times(
518.66/80.35	                ap(
518.66/80.35	                  d_Sigma(
518.66/80.35	                    d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                      (^[Y0 : $i]:
518.66/80.35	                         lessis(Y0, 
518.66/80.35	                           n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	                    (^[Y0 : $i]:
518.66/80.35	                       ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                         prop1(
518.66/80.35	                           (Y0 =
518.66/80.35	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                              ordsucc(emptyset))), 
518.66/80.35	                           d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                           ap(times(X98), X99), ap(times(X97), X99))))), 
518.66/80.35	                  outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                    ordsucc(emptyset)))), 
518.66/80.35	              ap(
518.66/80.35	                d_Sigma(
518.66/80.35	                  d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
518.66/80.35	                    (^[Y0 : $i]:
518.66/80.35	                       lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
518.66/80.35	                  (^[Y0 : $i]:
518.66/80.35	                     ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
518.66/80.35	                       prop1(
518.66/80.35	                         (Y0 =
518.66/80.35	                          outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                            ordsucc(emptyset))), 
518.66/80.35	                         d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), X98, 
518.66/80.35	                         X97)))), n_2t))
518.66/80.35	       | ~ is_of(X99, 
518.66/80.35	             (^[Y0 : $i]:
518.66/80.35	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
518.66/80.35	       | ~ is_of(X98, 
518.66/80.35	             (^[Y0 : $i]:
518.66/80.35	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
518.66/80.35	    inference('cnf', [status(esa)], [zf_stmt_4])).
518.66/80.35	tff('75', plain, ![X24, X27]: '#l_lift36444'(X24, X27) = in(X27, X24),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('76', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('77', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('78', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('79', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('80', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('81', plain,
518.66/80.35	    ![X100]:
518.66/80.35	      '#l_lift36446'(X100)
518.66/80.35	       = lessis(X100, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('82', plain,
518.66/80.35	    ![X97, X98, X101]:
518.66/80.35	      '#l_lift36447'(X97, X98, X101)
518.66/80.35	       = ind(d_Sep(omega, '#l_lift36445'), 
518.66/80.35	           prop1(
518.66/80.35	             (X101 =
518.66/80.35	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                ordsucc(emptyset))), d_Sep(omega, '#l_lift36445'), X98, X97)),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('83', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('84', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('85', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('86', plain,
518.66/80.35	    ![X100]:
518.66/80.35	      '#l_lift36446'(X100)
518.66/80.35	       = lessis(X100, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('87', plain,
518.66/80.35	    ![X97, X98, X101]:
518.66/80.35	      '#l_lift36447'(X97, X98, X101)
518.66/80.35	       = ind(d_Sep(omega, '#l_lift36445'), 
518.66/80.35	           prop1(
518.66/80.35	             (X101 =
518.66/80.35	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                ordsucc(emptyset))), d_Sep(omega, '#l_lift36445'), X98, X97)),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('88', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('89', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('90', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('91', plain,
518.66/80.35	    ![X100]:
518.66/80.35	      '#l_lift36446'(X100)
518.66/80.35	       = lessis(X100, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('92', plain,
518.66/80.35	    ![X97, X98, X101]:
518.66/80.35	      '#l_lift36447'(X97, X98, X101)
518.66/80.35	       = ind(d_Sep(omega, '#l_lift36445'), 
518.66/80.35	           prop1(
518.66/80.35	             (X101 =
518.66/80.35	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                ordsucc(emptyset))), d_Sep(omega, '#l_lift36445'), X98, X97)),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('93', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('94', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('95', plain, ![X24, X27]: '#l_lift36444'(X24, X27) = in(X27, X24),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('96', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('97', plain, ![X24, X27]: '#l_lift36444'(X24, X27) = in(X27, X24),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('98', plain, ![X72]: '#l_lift36445'(X72) = (X72 != emptyset),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('99', plain,
518.66/80.35	    ![X100]:
518.66/80.35	      '#l_lift36446'(X100)
518.66/80.35	       = lessis(X100, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('100', plain,
518.66/80.35	    ![X97, X98, X101]:
518.66/80.35	      '#l_lift36447'(X97, X98, X101)
518.66/80.35	       = ind(d_Sep(omega, '#l_lift36445'), 
518.66/80.35	           prop1(
518.66/80.35	             (X101 =
518.66/80.35	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                ordsucc(emptyset))), d_Sep(omega, '#l_lift36445'), X98, X97)),
518.66/80.35	    define([status(thm)])).
518.66/80.35	tff('101', plain,
518.66/80.35	    ![X97, X98, X99]:
518.66/80.35	      (~ is_of(X97, '#l_lift36444'(d_Sep(omega, '#l_lift36445')))
518.66/80.35	       | ap(
518.66/80.35	           times(
518.66/80.35	             ap(
518.66/80.35	               d_Sigma(d_Sep(d_Sep(omega, '#l_lift36445'), '#l_lift36446'), 
518.66/80.35	                 '#l_lift36447'(X97, X98)), 
518.66/80.35	               outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                 ordsucc(emptyset)))), 
518.66/80.35	           ap(
518.66/80.35	             d_Sigma(d_Sep(d_Sep(omega, '#l_lift36445'), '#l_lift36446'), 
518.66/80.35	               '#l_lift36447'(ap(times(X97), X99), ap(times(X98), X99))), 
518.66/80.35	             n_2t))
518.66/80.35	          = ap(
518.66/80.35	              times(
518.66/80.35	                ap(
518.66/80.35	                  d_Sigma(
518.66/80.35	                    d_Sep(d_Sep(omega, '#l_lift36445'), '#l_lift36446'), 
518.66/80.35	                    '#l_lift36447'(ap(times(X97), X99), ap(times(X98), X99))), 
518.66/80.35	                  outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
518.66/80.35	                    ordsucc(emptyset)))), 
518.66/80.35	              ap(
518.66/80.35	                d_Sigma(d_Sep(d_Sep(omega, '#l_lift36445'), '#l_lift36446'), 
518.66/80.35	                  '#l_lift36447'(X97, X98)), n_2t))
518.66/80.35	       | ~ is_of(X99, '#l_lift36444'(d_Sep(omega, '#l_lift36445')))
518.66/80.35	       | ~ is_of(X98, '#l_lift36444'(d_Sep(omega, '#l_lift36445')))),
518.66/80.35	    inference('lambda_lifting', [status(thm)],
518.66/80.35	              ['74', '75', '76', '77', '78', '79', '80', '81', '82', '83', 
518.66/80.35	               '84', '85', '86', '87', '88', '89', '90', '91', '92', '93', 
518.66/80.35	               '94', '95', '96', '97', '98', '99', '100'])).
518.66/80.35	tff('102', plain, $false,
518.66/80.35	    inference('eprover', [status(thm)], ['41', '45', '49', '73', '101'])).
518.66/80.35	
518.66/80.35	% SZS output end Refutation
518.66/80.35	
518.66/80.35	
518.66/80.35	% Terminating...
519.44/80.44	% Runner terminated.
519.44/80.45	% Zipperpin 1.5 exiting
519.44/80.45	EOF