0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.16	% Command    : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.aoUezaAbBs
0.16/0.36	% Computer   : n010.cluster.edu
0.16/0.36	% Model      : x86_64 x86_64
0.16/0.36	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.16/0.36	% Memory     : 8042.1875MB
0.16/0.36	% OS         : Linux 3.10.0-693.el7.x86_64
0.16/0.36	% CPULimit   : 960
0.16/0.36	% DateTime   : Thu Jul  2 09:10:31 EDT 2020
0.16/0.37	% CPUTime    : 
0.16/0.37	% Running portfolio for 120 s
0.16/0.37	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.16/0.37	% Number of cores: 8
0.16/0.37	% Python version: Python 3.6.8
0.16/0.37	% Running in HO mode
0.56/0.64	% Estimated wc time : 1286
0.56/0.64	% Estimated cpu time (7 cpus) : 183.71428571428572
0.57/0.72	% /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s
0.57/0.73	% /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s
0.57/0.73	% /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s
0.57/0.75	% /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s
0.57/0.75	% /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s
0.57/0.76	% /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s
0.58/0.79	% /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s
71.27/11.11	% /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s
104.32/15.84	% /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s
104.32/15.85	% /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s
143.43/21.58	% /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s
143.89/21.66	% /export/starexec/sandbox2/solver/bin/lams/b.split.sh running for 31s
180.58/26.94	% /export/starexec/sandbox2/solver/bin/lams/s4.sh running for 15s
189.98/28.30	% /export/starexec/sandbox2/solver/bin/lams/b.rw.sh running for 26s
258.90/38.41	% /export/starexec/sandbox2/solver/bin/lams/c_ic.sh running for 42s
284.52/42.22	% /export/starexec/sandbox2/solver/bin/lams/s1.f.sh running for 15s
285.11/42.34	% /export/starexec/sandbox2/solver/bin/lams/c.preprocess2.sh running for 21s
351.80/52.86	% /export/starexec/sandbox2/solver/bin/lams/sh.or.sh running for 26s
360.91/54.42	% /export/starexec/sandbox2/solver/bin/lams/new.cs3.comb.sh running for 18s
377.09/57.26	% /export/starexec/sandbox2/solver/bin/lams/old_b2.sh running for 31s
388.47/59.20	% /export/starexec/sandbox2/solver/bin/lams/sp5.sh running for 36s
417.73/63.50	% /export/starexec/sandbox2/solver/bin/lams/b2.sh running for 15s
454.16/68.81	% /export/starexec/sandbox2/solver/bin/lams/b.lcnf.od.sh running for 26s
480.10/72.58	% /export/starexec/sandbox2/solver/bin/lams/c.s.sh running for 36s
521.49/78.52	% /export/starexec/sandbox2/solver/bin/lams/b3.sh running for 26s
525.06/79.02	% /export/starexec/sandbox2/solver/bin/lams/cmb.lcnf.sh running for 10s
531.69/80.07	% Solved by lams/c.s.sh.
531.69/80.07	% Running : timeout 27 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.aoUezaAbBs/e_inputf5428a --cpu-limit=25 --auto-schedule -s -p.
531.69/80.07	% done 761 iterations in 7.454s
531.69/80.07	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
531.69/80.07	% SZS output start Refutation
531.69/80.07	tff(def_n_eq, axiom, n_eq() =
531.69/80.07	  ^[X0,X1]: n_is(n_ts(num(X0),den(X1)),n_ts(num(X1),den(X0)))).
531.69/80.07	tff(def_den, axiom, den() = second1(nat)).
531.69/80.07	tff(def_second1, axiom, second1() = ^[X0,X1]: ap(X1,n_2t)).
531.69/80.07	tff(def_n_2t, axiom, n_2t() = outn(n_2,n_2)).
531.69/80.07	tff(def_n_2, axiom, n_2() = n_pl(n_1,n_1)).
531.69/80.07	tff(def_n_1, axiom, n_1() = ordsucc(emptyset)).
531.69/80.07	tff('0', plain, n_1 = ordsucc(emptyset),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_n_1])).
531.69/80.07	tff('1', plain, n_1 = ordsucc(emptyset), define([status(thm)])).
531.69/80.07	tff('2', plain, n_2 = n_pl(n_1,n_1),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_n_2, '1'])).
531.69/80.07	tff('3', plain, n_2 = n_pl(n_1,n_1), define([status(thm)])).
531.69/80.07	tff('4', plain, n_2t = outn(n_2,n_2),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_n_2t, '3', '1'])).
531.69/80.07	tff('5', plain, n_2t = outn(n_2,n_2), define([status(thm)])).
531.69/80.07	tff('6', plain, second1 = (^[X0,X1]: ap(X1,n_2t)),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_second1, '5', '3', '1'])).
531.69/80.07	tff('7', plain, second1 = (^[V_1,V_2]: ap(V_2,n_2t)), define([status(thm)])).
531.69/80.07	tff(def_nat, axiom, nat() = d_Sep(omega,^[X0]: (X0 != emptyset))).
531.69/80.07	tff('8', plain, nat = d_Sep(omega,^[X0]: (X0 != emptyset)),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_nat])).
531.69/80.07	tff('9', plain, nat = d_Sep(omega,^[V_1]: (V_1 != emptyset)),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('10', plain, den = second1(nat),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_den, '7', '5', '9'])).
531.69/80.07	tff('11', plain, den = second1(nat), define([status(thm)])).
531.69/80.07	tff(def_num, axiom, num() = first1(nat)).
531.69/80.07	tff(def_first1, axiom, first1() = ^[X0,X1]: ap(X1,n_1t)).
531.69/80.07	tff(def_n_1t, axiom, n_1t() = outn(n_2,n_1)).
531.69/80.07	tff('12', plain, n_1t = outn(n_2,n_1),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_n_1t, '3', '1'])).
531.69/80.07	tff('13', plain, n_1t = outn(n_2,n_1), define([status(thm)])).
531.69/80.07	tff('14', plain, first1 = (^[X0,X1]: ap(X1,n_1t)),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_first1, '13', '3', '1'])).
531.69/80.07	tff('15', plain, first1 = (^[V_1,V_2]: ap(V_2,n_1t)), define([status(thm)])).
531.69/80.07	tff('16', plain, num = first1(nat),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_num, '15', '13', '9'])).
531.69/80.07	tff('17', plain, num = first1(nat), define([status(thm)])).
531.69/80.07	tff(def_n_ts, axiom, n_ts() = ^[X0]: ap(times(X0))).
531.69/80.07	tff('18', plain, n_ts = (^[X0]: ap(times(X0))),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_n_ts])).
531.69/80.07	tff('19', plain, n_ts = (^[V_1]: ap(times(V_1))), define([status(thm)])).
531.69/80.07	tff(def_n_is, axiom, n_is() = e_is(nat)).
531.69/80.07	tff(def_e_is, axiom, e_is() = ^[X0,X,Y]: (X = Y)).
531.69/80.07	tff('20', plain, e_is = (^[X0,X,Y]: (X = Y)),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_e_is])).
531.69/80.07	tff('21', plain, e_is = (^[V_1,V_2,V_3]: (V_2 = V_3)), define([status(thm)])).
531.69/80.07	tff('22', plain, n_is = e_is(nat),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_n_is, '9', '21'])).
531.69/80.07	tff('23', plain, n_is = e_is(nat), define([status(thm)])).
531.69/80.07	tff('24', plain,
531.69/80.07	    n_eq = (^[X0,X1]: n_is(n_ts(num(X0),den(X1)),n_ts(num(X1),den(X0)))),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)],
531.69/80.07	              [def_n_eq, '11', '17', '7', '15', '5', '13', '3', '19', '1', 
531.69/80.07	               '23', '9', '21'])).
531.69/80.07	tff('25', plain,
531.69/80.07	    n_eq =
531.69/80.07	    (^[V_1,V_2]: n_is(n_ts(num(V_1),den(V_2)),n_ts(num(V_2),den(V_1)))),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff(def_n_fr, axiom, n_fr() = pair1(nat)).
531.69/80.07	tff(def_pair1, axiom, pair1() =
531.69/80.07	  ^[X0,X1,X2]:
531.69/80.07	    d_Sigma(d_1to(n_2),^[X3]: ite(e_is(d_1to(n_2),X3,n_1t),X0,X1,X2))).
531.69/80.07	tff(def_d_1to, axiom, d_1to() = ^[X0]: d_Sep(nat,^[X1]: lessis(X1,X0))).
531.69/80.07	tff('26', plain, d_1to = (^[X0]: d_Sep(nat,^[X1]: lessis(X1,X0))),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_d_1to, '9'])).
531.69/80.07	tff('27', plain, d_1to = (^[V_1]: d_Sep(nat,^[V_2]: lessis(V_2,V_1))),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff(def_ite, axiom, ite() = ^[X0:$o,X1,X2,X3]: ind(X1,prop1(X0,X1,X2,X3))).
531.69/80.07	tff('28', plain, ite = (^[X0:$o,X1,X2,X3]: ind(X1,prop1(X0,X1,X2,X3))),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_ite])).
531.69/80.07	tff('29', plain,
531.69/80.07	    ite = (^[V_1:$o,V_2,V_3,V_4]: ind(V_2,prop1(V_1,V_2,V_3,V_4))),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('30', plain,
531.69/80.07	    pair1 =
531.69/80.07	    (^[X0,X1,X2]:
531.69/80.07	       d_Sigma(d_1to(n_2),^[X3]: ite(e_is(d_1to(n_2),X3,n_1t),X0,X1,X2))),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)],
531.69/80.07	              [def_pair1, '13', '3', '27', '1', '9', '29', '21'])).
531.69/80.07	tff('31', plain,
531.69/80.07	    pair1 =
531.69/80.07	    (^[V_1,V_2,V_3]:
531.69/80.07	       d_Sigma(d_1to(n_2),^[V_4]: ite(e_is(d_1to(n_2),V_4,n_1t),V_1,V_2,V_3))),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('32', plain, n_fr = pair1(nat),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)],
531.69/80.07	              [def_n_fr, '31', '13', '3', '27', '1', '9', '29', '21'])).
531.69/80.07	tff('33', plain, n_fr = pair1(nat), define([status(thm)])).
531.69/80.07	tff(def_frac, axiom, frac() = pair1type(nat)).
531.69/80.07	tff('34', plain, frac = pair1type(nat),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_frac, '9'])).
531.69/80.07	tff('35', plain, frac = pair1type(nat), define([status(thm)])).
531.69/80.07	tff(def_all_of, axiom, all_of() =
531.69/80.07	  ^[X0:(($i > $o)),X1:(($i > $o))]: (![X2]: (is_of(X2,X0) => X1(X2)))).
531.69/80.07	tff('36', plain,
531.69/80.07	    all_of =
531.69/80.07	    (^[X0:(($i > $o)),X1:(($i > $o))]: (![X2]: (is_of(X2,X0) => X1(X2)))),
531.69/80.07	    inference('simplify_rw_rule', [status(thm)], [def_all_of])).
531.69/80.07	tff('37', plain,
531.69/80.07	    all_of =
531.69/80.07	    (^[V_1:(($i > $o)),V_2:(($i > $o))]: (![X4]: (is_of(X4,V_1) => V_2(X4)))),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff(satz40a, conjecture,
531.69/80.07	  (all_of(^[X0]: in(X0,frac),
531.69/80.07	          ^[X0]:
531.69/80.07	            all_of(^[X1]: in(X1,nat),
531.69/80.07	                   ^[X1]: n_eq(n_fr(n_ts(num(X0),X1),n_ts(den(X0),X1)),X0))))).
531.69/80.07	tff(zf_stmt_0, conjecture,
531.69/80.07	  (![X4]:
531.69/80.07	     (is_of(X4,
531.69/80.07	            ^[V_1]: in(V_1,pair1type(d_Sep(omega,^[V_2]: (V_2 != emptyset))))) =>
531.69/80.07	      (![X6]:
531.69/80.07	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
531.69/80.07	          (ap(times(ap(d_Sigma(d_Sep(d_Sep(omega,^[V_5]: (V_5 != emptyset)),
531.69/80.07	                                     ^[V_6]:
531.69/80.07	                                       lessis(V_6,
531.69/80.07	                                              n_pl(ordsucc(emptyset),
531.69/80.07	                                                   ordsucc(emptyset)))),
531.69/80.07	                               ^[V_7]:
531.69/80.07	                                 ind(d_Sep(omega,^[V_8]: (V_8 != emptyset)),
531.69/80.07	                                     prop1(V_7 =
531.69/80.07	                                           outn(n_pl(ordsucc(emptyset),
531.69/80.07	                                                     ordsucc(emptyset)),
531.69/80.07	                                                ordsucc(emptyset)),
531.69/80.07	                                           d_Sep(omega,
531.69/80.07	                                                 ^[V_9]: (V_9 != emptyset)),
531.69/80.07	                                           ap(times(ap(X4,
531.69/80.07	                                                       outn(n_pl(ordsucc(
531.69/80.07	                                                                 emptyset),
531.69/80.07	                                                                 ordsucc(
531.69/80.07	                                                                 emptyset)),
531.69/80.07	                                                            ordsucc(emptyset)))),
531.69/80.07	                                              X6),
531.69/80.07	                                           ap(times(ap(X4,
531.69/80.07	                                                       outn(n_pl(ordsucc(
531.69/80.07	                                                                 emptyset),
531.69/80.07	                                                                 ordsucc(
531.69/80.07	                                                                 emptyset)),
531.69/80.07	                                                            n_pl(ordsucc(
531.69/80.07	                                                                 emptyset),
531.69/80.07	                                                                 ordsucc(
531.69/80.07	                                                                 emptyset))))),
531.69/80.07	                                              X6)))),
531.69/80.07	                       outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                            ordsucc(emptyset)))),
531.69/80.07	              ap(X4,
531.69/80.07	                 outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                      n_pl(ordsucc(emptyset),ordsucc(emptyset))))) =
531.69/80.07	           ap(times(ap(X4,
531.69/80.07	                       outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                            ordsucc(emptyset)))),
531.69/80.07	              ap(d_Sigma(d_Sep(d_Sep(omega,^[V_10]: (V_10 != emptyset)),
531.69/80.07	                               ^[V_11]:
531.69/80.07	                                 lessis(V_11,
531.69/80.07	                                        n_pl(ordsucc(emptyset),
531.69/80.07	                                             ordsucc(emptyset)))),
531.69/80.07	                         ^[V_12]:
531.69/80.07	                           ind(d_Sep(omega,^[V_13]: (V_13 != emptyset)),
531.69/80.07	                               prop1(V_12 =
531.69/80.07	                                     outn(n_pl(ordsucc(emptyset),
531.69/80.07	                                               ordsucc(emptyset)),
531.69/80.07	                                          ordsucc(emptyset)),
531.69/80.07	                                     d_Sep(omega,^[V_14]: (V_14 != emptyset)),
531.69/80.07	                                     ap(times(ap(X4,
531.69/80.07	                                                 outn(n_pl(ordsucc(emptyset),
531.69/80.07	                                                           ordsucc(emptyset)),
531.69/80.07	                                                      ordsucc(emptyset)))),
531.69/80.07	                                        X6),
531.69/80.07	                                     ap(times(ap(X4,
531.69/80.07	                                                 outn(n_pl(ordsucc(emptyset),
531.69/80.07	                                                           ordsucc(emptyset)),
531.69/80.07	                                                      n_pl(ordsucc(emptyset),
531.69/80.07	                                                           ordsucc(emptyset))))),
531.69/80.07	                                        X6)))),
531.69/80.07	                 outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                      n_pl(ordsucc(emptyset),ordsucc(emptyset))))))))))).
531.69/80.07	tff(zf_stmt_1, negated_conjecture,
531.69/80.07	  (~
531.69/80.07	    (![X4]:
531.69/80.07	       (is_of(X4,
531.69/80.07	              ^[V_1]:
531.69/80.07	                in(V_1,pair1type(d_Sep(omega,^[V_2]: (V_2 != emptyset))))) =>
531.69/80.07	        (![X6]:
531.69/80.07	           (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
531.69/80.07	            (ap(times(ap(d_Sigma(d_Sep(d_Sep(omega,^[V_5]: (V_5 != emptyset)),
531.69/80.07	                                       ^[V_6]:
531.69/80.07	                                         lessis(V_6,
531.69/80.07	                                                n_pl(ordsucc(emptyset),
531.69/80.07	                                                     ordsucc(emptyset)))),
531.69/80.07	                                 ^[V_7]:
531.69/80.07	                                   ind(d_Sep(omega,^[V_8]: (V_8 != emptyset)),
531.69/80.07	                                       prop1(V_7 =
531.69/80.07	                                             outn(n_pl(ordsucc(emptyset),
531.69/80.07	                                                       ordsucc(emptyset)),
531.69/80.07	                                                  ordsucc(emptyset)),
531.69/80.07	                                             d_Sep(omega,
531.69/80.07	                                                   ^[V_9]: (V_9 != emptyset)),
531.69/80.07	                                             ap(times(ap(X4,
531.69/80.07	                                                         outn(n_pl(ordsucc(
531.69/80.07	                                                                   emptyset),
531.69/80.07	                                                                   ordsucc(
531.69/80.07	                                                                   emptyset)),
531.69/80.07	                                                              ordsucc(
531.69/80.07	                                                              emptyset)))),
531.69/80.07	                                                X6),
531.69/80.07	                                             ap(times(ap(X4,
531.69/80.07	                                                         outn(n_pl(ordsucc(
531.69/80.07	                                                                   emptyset),
531.69/80.07	                                                                   ordsucc(
531.69/80.07	                                                                   emptyset)),
531.69/80.07	                                                              n_pl(ordsucc(
531.69/80.07	                                                                   emptyset),
531.69/80.07	                                                                   ordsucc(
531.69/80.07	                                                                   emptyset))))),
531.69/80.07	                                                X6)))),
531.69/80.07	                         outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                              ordsucc(emptyset)))),
531.69/80.07	                ap(X4,
531.69/80.07	                   outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                        n_pl(ordsucc(emptyset),ordsucc(emptyset))))) =
531.69/80.07	             ap(times(ap(X4,
531.69/80.07	                         outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                              ordsucc(emptyset)))),
531.69/80.07	                ap(d_Sigma(d_Sep(d_Sep(omega,^[V_10]: (V_10 != emptyset)),
531.69/80.07	                                 ^[V_11]:
531.69/80.07	                                   lessis(V_11,
531.69/80.07	                                          n_pl(ordsucc(emptyset),
531.69/80.07	                                               ordsucc(emptyset)))),
531.69/80.07	                           ^[V_12]:
531.69/80.07	                             ind(d_Sep(omega,^[V_13]: (V_13 != emptyset)),
531.69/80.07	                                 prop1(V_12 =
531.69/80.07	                                       outn(n_pl(ordsucc(emptyset),
531.69/80.07	                                                 ordsucc(emptyset)),
531.69/80.07	                                            ordsucc(emptyset)),
531.69/80.07	                                       d_Sep(omega,
531.69/80.07	                                             ^[V_14]: (V_14 != emptyset)),
531.69/80.07	                                       ap(times(ap(X4,
531.69/80.07	                                                   outn(n_pl(ordsucc(
531.69/80.07	                                                             emptyset),
531.69/80.07	                                                             ordsucc(
531.69/80.07	                                                             emptyset)),
531.69/80.07	                                                        ordsucc(emptyset)))),
531.69/80.07	                                          X6),
531.69/80.07	                                       ap(times(ap(X4,
531.69/80.07	                                                   outn(n_pl(ordsucc(
531.69/80.07	                                                             emptyset),
531.69/80.07	                                                             ordsucc(
531.69/80.07	                                                             emptyset)),
531.69/80.07	                                                        n_pl(ordsucc(
531.69/80.07	                                                             emptyset),
531.69/80.07	                                                             ordsucc(
531.69/80.07	                                                             emptyset))))),
531.69/80.07	                                          X6)))),
531.69/80.07	                   outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                        n_pl(ordsucc(emptyset),ordsucc(emptyset)))))))))))).
531.69/80.07	tff('38', plain,
531.69/80.07	     is_of(sk_X6, 
531.69/80.07	       (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))),
531.69/80.07	    inference('cnf', [status(esa)], [zf_stmt_1])).
531.69/80.07	tff(e_fisi, axiom,
531.69/80.07	  (![X0,X1]:
531.69/80.07	     all_of(^[X2]: in(X2,d_Pi(X0,^[X3]: X1)),
531.69/80.07	            ^[X2]:
531.69/80.07	              all_of(^[X3]: in(X3,d_Pi(X0,^[X4]: X1)),
531.69/80.07	                     ^[X3]:
531.69/80.07	                       (all_of(^[X4]: in(X4,X0),
531.69/80.07	                               ^[X4]: e_is(X1,ap(X2,X4),ap(X3,X4))) =>
531.69/80.07	                        e_is(d_Pi(X0,^[X4]: X1),X2,X3)))))).
531.69/80.07	tff(zf_stmt_2, axiom,
531.69/80.07	  (![X4,X6,X8]:
531.69/80.07	     (is_of(X8,^[V_1]: in(V_1,d_Pi(X4,^[V_2]: X6))) =>
531.69/80.07	      (![X10]:
531.69/80.07	         (is_of(X10,^[V_3]: in(V_3,d_Pi(X4,^[V_4]: X6))) =>
531.69/80.07	          ((![X12]:
531.69/80.07	              (is_of(X12,^[V_5]: in(V_5,X4)) => (ap(X8,X12) = ap(X10,X12)))) =>
531.69/80.07	           (X8 = X10))))))).
531.69/80.07	tff('39', plain,
531.69/80.07	    ![X23, X24, X25, X26]:
531.69/80.07	      (~ is_of(X23, (^[Y0 : $i]: in(Y0, d_Pi(X24, (^[Y1 : $i]: X25)))))
531.69/80.07	       | X26 = X23
531.69/80.07	       |  is_of(sk_X12(X23, X26, X24), (^[Y0 : $i]: in(Y0, X24)))
531.69/80.07	       | ~ is_of(X26, (^[Y0 : $i]: in(Y0, d_Pi(X24, (^[Y1 : $i]: X25)))))),
531.69/80.07	    inference('cnf', [status(esa)], [zf_stmt_2])).
531.69/80.07	tff('40', plain, ![X24, X27]: '#l_lift44747'(X24, X27) = in(X27, X24),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff(satz32c, axiom,
531.69/80.07	  (all_of(^[X0]: in(X0,nat),
531.69/80.07	          ^[X0]:
531.69/80.07	            all_of(^[X1]: in(X1,nat),
531.69/80.07	                   ^[X1]:
531.69/80.07	                     all_of(^[X2]: in(X2,nat),
531.69/80.07	                            ^[X2]:
531.69/80.07	                              (iii(X0,X1) => iii(n_ts(X0,X2),n_ts(X1,X2)))))))).
531.69/80.07	tff(zf_stmt_3, axiom,
531.69/80.07	  (![X4]:
531.69/80.07	     (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
531.69/80.07	      (![X6]:
531.69/80.07	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
531.69/80.07	          (![X8]:
531.69/80.07	             (is_of(X8,^[V_5]: in(V_5,d_Sep(omega,^[V_6]: (V_6 != emptyset)))) =>
531.69/80.07	              (iii(X4,X6) => iii(ap(times(X4),X8),ap(times(X6),X8)))))))))).
531.69/80.07	tff('41', plain,
531.69/80.07	    ![X73, X74, X75]:
531.69/80.07	      (~ is_of(X73, 
531.69/80.07	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
531.69/80.07	       | ~ iii(X74, X73)
531.69/80.07	       |  iii(ap(times(X74), X75), ap(times(X73), X75))
531.69/80.07	       | ~ is_of(X75, 
531.69/80.07	             (^[Y0 : $i]:
531.69/80.07	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
531.69/80.07	       | ~ is_of(X74, 
531.69/80.07	             (^[Y0 : $i]:
531.69/80.07	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
531.69/80.07	    inference('cnf', [status(esa)], [zf_stmt_3])).
531.69/80.07	tff('42', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('43', plain,  is_of(sk_X6, '#l_lift44747'(d_Sep(omega, '#l_lift44748'))),
531.69/80.07	    inference('lambda_lifting', [status(thm)], ['38', '40', '42'])).
531.69/80.07	tff('44', plain,
531.69/80.07	     is_of(sk_X4, 
531.69/80.07	       (^[Y0 : $i]:
531.69/80.07	          in(Y0, pair1type(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
531.69/80.07	    inference('cnf', [status(esa)], [zf_stmt_1])).
531.69/80.07	tff('45', plain, ![X24, X27]: '#l_lift44747'(X24, X27) = in(X27, X24),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('46', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('47', plain,
531.69/80.07	     is_of(sk_X4, '#l_lift44747'(pair1type(d_Sep(omega, '#l_lift44748')))),
531.69/80.07	    inference('lambda_lifting', [status(thm)], ['44', '45', '46'])).
531.69/80.07	tff('48', plain,
531.69/80.07	    ap(
531.69/80.07	      times(
531.69/80.07	        ap(
531.69/80.07	          d_Sigma(
531.69/80.07	            d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
531.69/80.07	              (^[Y0 : $i]:
531.69/80.07	                 lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	            (^[Y0 : $i]:
531.69/80.07	               ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                 prop1(
531.69/80.07	                   (Y0 =
531.69/80.07	                    outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                      ordsucc(emptyset))), 
531.69/80.07	                   d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                   ap(
531.69/80.07	                     times(
531.69/80.07	                       ap(sk_X4, 
531.69/80.07	                         outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                           ordsucc(emptyset)))), sk_X6), 
531.69/80.07	                   ap(
531.69/80.07	                     times(
531.69/80.07	                       ap(sk_X4, 
531.69/80.07	                         outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                           n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	                     sk_X6))))), 
531.69/80.07	          outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), ordsucc(emptyset)))), 
531.69/80.07	      ap(sk_X4, 
531.69/80.07	        outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	          n_pl(ordsucc(emptyset), ordsucc(emptyset)))))
531.69/80.07	     != ap(
531.69/80.07	          times(
531.69/80.07	            ap(sk_X4, 
531.69/80.07	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                ordsucc(emptyset)))), 
531.69/80.07	          ap(
531.69/80.07	            d_Sigma(
531.69/80.07	              d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
531.69/80.07	                (^[Y0 : $i]:
531.69/80.07	                   lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	              (^[Y0 : $i]:
531.69/80.07	                 ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                   prop1(
531.69/80.07	                     (Y0 =
531.69/80.07	                      outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                        ordsucc(emptyset))), 
531.69/80.07	                     d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                     ap(
531.69/80.07	                       times(
531.69/80.07	                         ap(sk_X4, 
531.69/80.07	                           outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                             ordsucc(emptyset)))), sk_X6), 
531.69/80.07	                     ap(
531.69/80.07	                       times(
531.69/80.07	                         ap(sk_X4, 
531.69/80.07	                           outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                             n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	                       sk_X6))))), 
531.69/80.07	            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	              n_pl(ordsucc(emptyset), ordsucc(emptyset))))),
531.69/80.07	    inference('cnf', [status(esa)], [zf_stmt_1])).
531.69/80.07	tff('49', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff(satz40, axiom,
531.69/80.07	  (all_of(^[X0]: in(X0,frac),
531.69/80.07	          ^[X0]:
531.69/80.07	            all_of(^[X1]: in(X1,nat),
531.69/80.07	                   ^[X1]: n_eq(X0,n_fr(n_ts(num(X0),X1),n_ts(den(X0),X1))))))).
531.69/80.07	tff(zf_stmt_4, axiom,
531.69/80.07	  (![X4]:
531.69/80.07	     (is_of(X4,
531.69/80.07	            ^[V_1]: in(V_1,pair1type(d_Sep(omega,^[V_2]: (V_2 != emptyset))))) =>
531.69/80.07	      (![X6]:
531.69/80.07	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
531.69/80.07	          (ap(times(ap(X4,
531.69/80.07	                       outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                            ordsucc(emptyset)))),
531.69/80.07	              ap(d_Sigma(d_Sep(d_Sep(omega,^[V_5]: (V_5 != emptyset)),
531.69/80.07	                               ^[V_6]:
531.69/80.07	                                 lessis(V_6,
531.69/80.07	                                        n_pl(ordsucc(emptyset),
531.69/80.07	                                             ordsucc(emptyset)))),
531.69/80.07	                         ^[V_7]:
531.69/80.07	                           ind(d_Sep(omega,^[V_8]: (V_8 != emptyset)),
531.69/80.07	                               prop1(V_7 =
531.69/80.07	                                     outn(n_pl(ordsucc(emptyset),
531.69/80.07	                                               ordsucc(emptyset)),
531.69/80.07	                                          ordsucc(emptyset)),
531.69/80.07	                                     d_Sep(omega,^[V_9]: (V_9 != emptyset)),
531.69/80.07	                                     ap(times(ap(X4,
531.69/80.07	                                                 outn(n_pl(ordsucc(emptyset),
531.69/80.07	                                                           ordsucc(emptyset)),
531.69/80.07	                                                      ordsucc(emptyset)))),
531.69/80.07	                                        X6),
531.69/80.07	                                     ap(times(ap(X4,
531.69/80.07	                                                 outn(n_pl(ordsucc(emptyset),
531.69/80.07	                                                           ordsucc(emptyset)),
531.69/80.07	                                                      n_pl(ordsucc(emptyset),
531.69/80.07	                                                           ordsucc(emptyset))))),
531.69/80.07	                                        X6)))),
531.69/80.07	                 outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                      n_pl(ordsucc(emptyset),ordsucc(emptyset))))) =
531.69/80.07	           ap(times(ap(d_Sigma(d_Sep(d_Sep(omega,^[V_10]: (V_10 != emptyset)),
531.69/80.07	                                     ^[V_11]:
531.69/80.07	                                       lessis(V_11,
531.69/80.07	                                              n_pl(ordsucc(emptyset),
531.69/80.07	                                                   ordsucc(emptyset)))),
531.69/80.07	                               ^[V_12]:
531.69/80.07	                                 ind(d_Sep(omega,^[V_13]: (V_13 != emptyset)),
531.69/80.07	                                     prop1(V_12 =
531.69/80.07	                                           outn(n_pl(ordsucc(emptyset),
531.69/80.07	                                                     ordsucc(emptyset)),
531.69/80.07	                                                ordsucc(emptyset)),
531.69/80.07	                                           d_Sep(omega,
531.69/80.07	                                                 ^[V_14]: (V_14 != emptyset)),
531.69/80.07	                                           ap(times(ap(X4,
531.69/80.07	                                                       outn(n_pl(ordsucc(
531.69/80.07	                                                                 emptyset),
531.69/80.07	                                                                 ordsucc(
531.69/80.07	                                                                 emptyset)),
531.69/80.07	                                                            ordsucc(emptyset)))),
531.69/80.07	                                              X6),
531.69/80.07	                                           ap(times(ap(X4,
531.69/80.07	                                                       outn(n_pl(ordsucc(
531.69/80.07	                                                                 emptyset),
531.69/80.07	                                                                 ordsucc(
531.69/80.07	                                                                 emptyset)),
531.69/80.07	                                                            n_pl(ordsucc(
531.69/80.07	                                                                 emptyset),
531.69/80.07	                                                                 ordsucc(
531.69/80.07	                                                                 emptyset))))),
531.69/80.07	                                              X6)))),
531.69/80.07	                       outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                            ordsucc(emptyset)))),
531.69/80.07	              ap(X4,
531.69/80.07	                 outn(n_pl(ordsucc(emptyset),ordsucc(emptyset)),
531.69/80.07	                      n_pl(ordsucc(emptyset),ordsucc(emptyset))))))))))).
531.69/80.07	tff('50', plain,
531.69/80.07	    ![X112, X113]:
531.69/80.07	      (~ is_of(X112, 
531.69/80.07	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
531.69/80.07	       | ap(
531.69/80.07	           times(
531.69/80.07	             ap(X113, 
531.69/80.07	               outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                 ordsucc(emptyset)))), 
531.69/80.07	           ap(
531.69/80.07	             d_Sigma(
531.69/80.07	               d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
531.69/80.07	                 (^[Y0 : $i]:
531.69/80.07	                    lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	               (^[Y0 : $i]:
531.69/80.07	                  ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                    prop1(
531.69/80.07	                      (Y0 =
531.69/80.07	                       outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                         ordsucc(emptyset))), 
531.69/80.07	                      d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                      ap(
531.69/80.07	                        times(
531.69/80.07	                          ap(X113, 
531.69/80.07	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                              ordsucc(emptyset)))), X112), 
531.69/80.07	                      ap(
531.69/80.07	                        times(
531.69/80.07	                          ap(X113, 
531.69/80.07	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                              n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	                        X112))))), 
531.69/80.07	             outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	               n_pl(ordsucc(emptyset), ordsucc(emptyset)))))
531.69/80.07	          = ap(
531.69/80.07	              times(
531.69/80.07	                ap(
531.69/80.07	                  d_Sigma(
531.69/80.07	                    d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
531.69/80.07	                      (^[Y0 : $i]:
531.69/80.07	                         lessis(Y0, 
531.69/80.07	                           n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	                    (^[Y0 : $i]:
531.69/80.07	                       ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                         prop1(
531.69/80.07	                           (Y0 =
531.69/80.07	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                              ordsucc(emptyset))), 
531.69/80.07	                           d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                           ap(
531.69/80.07	                             times(
531.69/80.07	                               ap(X113, 
531.69/80.07	                                 outn(
531.69/80.07	                                   n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                                   ordsucc(emptyset)))), X112), 
531.69/80.07	                           ap(
531.69/80.07	                             times(
531.69/80.07	                               ap(X113, 
531.69/80.07	                                 outn(
531.69/80.07	                                   n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                                   n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	                             X112))))), 
531.69/80.07	                  outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                    ordsucc(emptyset)))), 
531.69/80.07	              ap(X113, 
531.69/80.07	                outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                  n_pl(ordsucc(emptyset), ordsucc(emptyset)))))
531.69/80.07	       | ~ is_of(X113, 
531.69/80.07	             (^[Y0 : $i]:
531.69/80.07	                in(Y0, 
531.69/80.07	                  pair1type(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))))),
531.69/80.07	    inference('cnf', [status(esa)], [zf_stmt_4])).
531.69/80.07	tff('51', plain,
531.69/80.07	    ![X114]:
531.69/80.07	      '#l_lift44749'(X114)
531.69/80.07	       = lessis(X114, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('52', plain,
531.69/80.07	    ![X112, X113]:
531.69/80.07	      (~ is_of(X112, 
531.69/80.07	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
531.69/80.07	       | ap(
531.69/80.07	           times(
531.69/80.07	             ap(X113, 
531.69/80.07	               outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                 ordsucc(emptyset)))), 
531.69/80.07	           ap(
531.69/80.07	             d_Sigma(
531.69/80.07	               d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
531.69/80.07	                 (^[Y0 : $i]:
531.69/80.07	                    lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	               (^[Y0 : $i]:
531.69/80.07	                  ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                    prop1(
531.69/80.07	                      (Y0 =
531.69/80.07	                       outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                         ordsucc(emptyset))), 
531.69/80.07	                      d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                      ap(
531.69/80.07	                        times(
531.69/80.07	                          ap(X113, 
531.69/80.07	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                              ordsucc(emptyset)))), X112), 
531.69/80.07	                      ap(
531.69/80.07	                        times(
531.69/80.07	                          ap(X113, 
531.69/80.07	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                              n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	                        X112))))), 
531.69/80.07	             outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	               n_pl(ordsucc(emptyset), ordsucc(emptyset)))))
531.69/80.07	          = ap(
531.69/80.07	              times(
531.69/80.07	                ap(
531.69/80.07	                  d_Sigma(
531.69/80.07	                    d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
531.69/80.07	                      (^[Y0 : $i]:
531.69/80.07	                         lessis(Y0, 
531.69/80.07	                           n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	                    (^[Y0 : $i]:
531.69/80.07	                       ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                         prop1(
531.69/80.07	                           (Y0 =
531.69/80.07	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                              ordsucc(emptyset))), 
531.69/80.07	                           d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                           ap(
531.69/80.07	                             times(
531.69/80.07	                               ap(X113, 
531.69/80.07	                                 outn(
531.69/80.07	                                   n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                                   ordsucc(emptyset)))), X112), 
531.69/80.07	                           ap(
531.69/80.07	                             times(
531.69/80.07	                               ap(X113, 
531.69/80.07	                                 outn(
531.69/80.07	                                   n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                                   n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	                             X112))))), 
531.69/80.07	                  outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                    ordsucc(emptyset)))), 
531.69/80.07	              ap(X113, 
531.69/80.07	                outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                  n_pl(ordsucc(emptyset), ordsucc(emptyset)))))
531.69/80.07	       | ~ is_of(X113, 
531.69/80.07	             (^[Y0 : $i]:
531.69/80.07	                in(Y0, 
531.69/80.07	                  pair1type(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))))),
531.69/80.07	    inference('cnf', [status(esa)], [zf_stmt_4])).
531.69/80.07	tff('53', plain,
531.69/80.07	    ![X112, X113, X115]:
531.69/80.07	      '#l_lift44750'(X112, X113, X115)
531.69/80.07	       = ind(d_Sep(omega, '#l_lift44748'), 
531.69/80.07	           prop1(
531.69/80.07	             (X115 =
531.69/80.07	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                ordsucc(emptyset))), d_Sep(omega, '#l_lift44748'), 
531.69/80.07	             ap(
531.69/80.07	               times(
531.69/80.07	                 ap(X113, 
531.69/80.07	                   outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                     ordsucc(emptyset)))), X112), 
531.69/80.07	             ap(
531.69/80.07	               times(
531.69/80.07	                 ap(X113, 
531.69/80.07	                   outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                     n_pl(ordsucc(emptyset), ordsucc(emptyset))))), X112))),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('54', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('55', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('56', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('57', plain,
531.69/80.07	    ![X114]:
531.69/80.07	      '#l_lift44749'(X114)
531.69/80.07	       = lessis(X114, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('58', plain,
531.69/80.07	    ![X112, X113, X115]:
531.69/80.07	      '#l_lift44750'(X112, X113, X115)
531.69/80.07	       = ind(d_Sep(omega, '#l_lift44748'), 
531.69/80.07	           prop1(
531.69/80.07	             (X115 =
531.69/80.07	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                ordsucc(emptyset))), d_Sep(omega, '#l_lift44748'), 
531.69/80.07	             ap(
531.69/80.07	               times(
531.69/80.07	                 ap(X113, 
531.69/80.07	                   outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                     ordsucc(emptyset)))), X112), 
531.69/80.07	             ap(
531.69/80.07	               times(
531.69/80.07	                 ap(X113, 
531.69/80.07	                   outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                     n_pl(ordsucc(emptyset), ordsucc(emptyset))))), X112))),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('59', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('60', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.07	    define([status(thm)])).
531.69/80.07	tff('61', plain,
531.69/80.07	    ap(
531.69/80.07	      times(
531.69/80.07	        ap(
531.69/80.07	          d_Sigma(d_Sep(d_Sep(omega, '#l_lift44748'), '#l_lift44749'), 
531.69/80.07	            '#l_lift44750'(sk_X6, sk_X4)), 
531.69/80.07	          outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), ordsucc(emptyset)))), 
531.69/80.07	      ap(sk_X4, 
531.69/80.07	        outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	          n_pl(ordsucc(emptyset), ordsucc(emptyset)))))
531.69/80.07	     != ap(
531.69/80.07	          times(
531.69/80.07	            ap(sk_X4, 
531.69/80.07	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                ordsucc(emptyset)))), 
531.69/80.07	          ap(
531.69/80.07	            d_Sigma(d_Sep(d_Sep(omega, '#l_lift44748'), '#l_lift44749'), 
531.69/80.07	              '#l_lift44750'(sk_X6, sk_X4)), 
531.69/80.07	            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	              n_pl(ordsucc(emptyset), ordsucc(emptyset))))),
531.69/80.07	    inference('lambda_lifting', [status(thm)],
531.69/80.07	              ['48', '49', '51', '53', '54', '55', '56', '57', '58', '59', 
531.69/80.07	               '60'])).
531.69/80.07	tff('62', plain,
531.69/80.07	    ![X112, X113]:
531.69/80.07	      (~ is_of(X112, 
531.69/80.07	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
531.69/80.07	       | ap(
531.69/80.07	           times(
531.69/80.07	             ap(X113, 
531.69/80.07	               outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                 ordsucc(emptyset)))), 
531.69/80.07	           ap(
531.69/80.07	             d_Sigma(
531.69/80.07	               d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
531.69/80.07	                 (^[Y0 : $i]:
531.69/80.07	                    lessis(Y0, n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	               (^[Y0 : $i]:
531.69/80.07	                  ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                    prop1(
531.69/80.07	                      (Y0 =
531.69/80.07	                       outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                         ordsucc(emptyset))), 
531.69/80.07	                      d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                      ap(
531.69/80.07	                        times(
531.69/80.07	                          ap(X113, 
531.69/80.07	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                              ordsucc(emptyset)))), X112), 
531.69/80.07	                      ap(
531.69/80.07	                        times(
531.69/80.07	                          ap(X113, 
531.69/80.07	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                              n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	                        X112))))), 
531.69/80.07	             outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	               n_pl(ordsucc(emptyset), ordsucc(emptyset)))))
531.69/80.07	          = ap(
531.69/80.07	              times(
531.69/80.07	                ap(
531.69/80.07	                  d_Sigma(
531.69/80.07	                    d_Sep(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), 
531.69/80.07	                      (^[Y0 : $i]:
531.69/80.07	                         lessis(Y0, 
531.69/80.07	                           n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.07	                    (^[Y0 : $i]:
531.69/80.07	                       ind(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                         prop1(
531.69/80.07	                           (Y0 =
531.69/80.07	                            outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                              ordsucc(emptyset))), 
531.69/80.07	                           d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))), 
531.69/80.07	                           ap(
531.69/80.07	                             times(
531.69/80.07	                               ap(X113, 
531.69/80.07	                                 outn(
531.69/80.07	                                   n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.07	                                   ordsucc(emptyset)))), X112), 
531.69/80.07	                           ap(
531.69/80.07	                             times(
531.69/80.07	                               ap(X113, 
531.69/80.07	                                 outn(
531.69/80.07	                                   n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                                   n_pl(ordsucc(emptyset), ordsucc(emptyset))))), 
531.69/80.08	                             X112))))), 
531.69/80.08	                  outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                    ordsucc(emptyset)))), 
531.69/80.08	              ap(X113, 
531.69/80.08	                outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                  n_pl(ordsucc(emptyset), ordsucc(emptyset)))))
531.69/80.08	       | ~ is_of(X113, 
531.69/80.08	             (^[Y0 : $i]:
531.69/80.08	                in(Y0, 
531.69/80.08	                  pair1type(d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))))),
531.69/80.08	    inference('cnf', [status(esa)], [zf_stmt_4])).
531.69/80.08	tff('63', plain, ![X24, X27]: '#l_lift44747'(X24, X27) = in(X27, X24),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('64', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('65', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('66', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('67', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('68', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('69', plain,
531.69/80.08	    ![X114]:
531.69/80.08	      '#l_lift44749'(X114)
531.69/80.08	       = lessis(X114, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('70', plain,
531.69/80.08	    ![X112, X113, X115]:
531.69/80.08	      '#l_lift44750'(X112, X113, X115)
531.69/80.08	       = ind(d_Sep(omega, '#l_lift44748'), 
531.69/80.08	           prop1(
531.69/80.08	             (X115 =
531.69/80.08	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                ordsucc(emptyset))), d_Sep(omega, '#l_lift44748'), 
531.69/80.08	             ap(
531.69/80.08	               times(
531.69/80.08	                 ap(X113, 
531.69/80.08	                   outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                     ordsucc(emptyset)))), X112), 
531.69/80.08	             ap(
531.69/80.08	               times(
531.69/80.08	                 ap(X113, 
531.69/80.08	                   outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                     n_pl(ordsucc(emptyset), ordsucc(emptyset))))), X112))),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('71', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('72', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('73', plain, ![X24, X27]: '#l_lift44747'(X24, X27) = in(X27, X24),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('74', plain, ![X76]: '#l_lift44748'(X76) = (X76 != emptyset),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('75', plain,
531.69/80.08	    ![X114]:
531.69/80.08	      '#l_lift44749'(X114)
531.69/80.08	       = lessis(X114, n_pl(ordsucc(emptyset), ordsucc(emptyset))),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('76', plain,
531.69/80.08	    ![X112, X113, X115]:
531.69/80.08	      '#l_lift44750'(X112, X113, X115)
531.69/80.08	       = ind(d_Sep(omega, '#l_lift44748'), 
531.69/80.08	           prop1(
531.69/80.08	             (X115 =
531.69/80.08	              outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                ordsucc(emptyset))), d_Sep(omega, '#l_lift44748'), 
531.69/80.08	             ap(
531.69/80.08	               times(
531.69/80.08	                 ap(X113, 
531.69/80.08	                   outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                     ordsucc(emptyset)))), X112), 
531.69/80.08	             ap(
531.69/80.08	               times(
531.69/80.08	                 ap(X113, 
531.69/80.08	                   outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                     n_pl(ordsucc(emptyset), ordsucc(emptyset))))), X112))),
531.69/80.08	    define([status(thm)])).
531.69/80.08	tff('77', plain,
531.69/80.08	    ![X112, X113]:
531.69/80.08	      (~ is_of(X112, '#l_lift44747'(d_Sep(omega, '#l_lift44748')))
531.69/80.08	       | ap(
531.69/80.08	           times(
531.69/80.08	             ap(X113, 
531.69/80.08	               outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                 ordsucc(emptyset)))), 
531.69/80.08	           ap(
531.69/80.08	             d_Sigma(d_Sep(d_Sep(omega, '#l_lift44748'), '#l_lift44749'), 
531.69/80.08	               '#l_lift44750'(X112, X113)), 
531.69/80.08	             outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	               n_pl(ordsucc(emptyset), ordsucc(emptyset)))))
531.69/80.08	          = ap(
531.69/80.08	              times(
531.69/80.08	                ap(
531.69/80.08	                  d_Sigma(
531.69/80.08	                    d_Sep(d_Sep(omega, '#l_lift44748'), '#l_lift44749'), 
531.69/80.08	                    '#l_lift44750'(X112, X113)), 
531.69/80.08	                  outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                    ordsucc(emptyset)))), 
531.69/80.08	              ap(X113, 
531.69/80.08	                outn(n_pl(ordsucc(emptyset), ordsucc(emptyset)), 
531.69/80.08	                  n_pl(ordsucc(emptyset), ordsucc(emptyset)))))
531.69/80.08	       | ~ is_of(X113, 
531.69/80.08	             '#l_lift44747'(pair1type(d_Sep(omega, '#l_lift44748'))))),
531.69/80.08	    inference('lambda_lifting', [status(thm)],
531.69/80.08	              ['62', '63', '64', '65', '66', '67', '68', '69', '70', '71', 
531.69/80.08	               '72', '73', '74', '75', '76'])).
531.69/80.08	tff('78', plain, $false,
531.69/80.08	    inference('eprover', [status(thm)], ['43', '47', '61', '77'])).
531.69/80.08	
531.69/80.08	% SZS output end Refutation
531.69/80.08	
531.69/80.08	
531.69/80.08	% Terminating...
532.27/80.14	% Runner terminated.
532.27/80.15	% Zipperpin 1.5 exiting
532.27/80.15	EOF