0.00/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.13/0.16	% Command    : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.me5Q9irtQY
0.16/0.38	% Computer   : n012.cluster.edu
0.16/0.38	% Model      : x86_64 x86_64
0.16/0.38	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.16/0.38	% Memory     : 8042.1875MB
0.16/0.38	% OS         : Linux 3.10.0-693.el7.x86_64
0.16/0.38	% CPULimit   : 1200
0.16/0.38	% DateTime   : Tue Jul 13 15:41:31 EDT 2021
0.16/0.38	% CPUTime    : 
0.16/0.38	% Running portfolio for 120 s
0.16/0.38	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.16/0.38	% Number of cores: 8
0.16/0.38	% Python version: Python 3.6.8
0.16/0.39	% Running in HO mode
0.57/0.68	% Estimated wc time : 1286
0.57/0.68	% Estimated cpu time (7 cpus) : 183.71428571428572
0.60/0.74	% /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s
0.60/0.76	% /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s
0.60/0.76	% /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s
0.60/0.78	% /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s
0.60/0.78	% /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s
0.60/0.78	% /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s
0.60/0.79	% /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s
71.49/10.85	% /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s
73.85/11.28	% Solved by lams/c.s.2.sh.
73.85/11.28	% Running : timeout 52 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.me5Q9irtQY/e_input8b4323 --cpu-limit=50 --auto-schedule -s -p.
73.85/11.28	% done 674 iterations in 10.469s
73.85/11.28	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
73.85/11.28	% SZS output start Refutation
73.85/11.28	tff(def_iii, axiom, iii() = ^[X0,X1]: n_some(diffprop(X1,X0))).
73.85/11.28	tff('0', plain, iii = (^[X0,X1]: n_some(diffprop(X1,X0))),
73.85/11.28	    inference('simplify_rw_rule', [status(thm)], [def_iii])).
73.85/11.28	tff('1', plain, iii = (^[V_1,V_2]: n_some(diffprop(V_2,V_1))),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff(def_nat, axiom, nat() = d_Sep(omega,^[X0]: (X0 != emptyset))).
73.85/11.28	tff('2', plain, nat = d_Sep(omega,^[X0]: (X0 != emptyset)),
73.85/11.28	    inference('simplify_rw_rule', [status(thm)], [def_nat])).
73.85/11.28	tff('3', plain, nat = d_Sep(omega,^[V_1]: (V_1 != emptyset)),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff(def_all_of, axiom, all_of() =
73.85/11.28	  ^[X0:(($i > $o)),X1:(($i > $o))]: (![X2]: (is_of(X2,X0) => X1(X2)))).
73.85/11.28	tff('4', plain,
73.85/11.28	    all_of =
73.85/11.28	    (^[X0:(($i > $o)),X1:(($i > $o))]: (![X2]: (is_of(X2,X0) => X1(X2)))),
73.85/11.28	    inference('simplify_rw_rule', [status(thm)], [def_all_of])).
73.85/11.28	tff('5', plain,
73.85/11.28	    all_of =
73.85/11.28	    (^[V_1:(($i > $o)),V_2:(($i > $o))]: (![X4]: (is_of(X4,V_1) => V_2(X4)))),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff(satz11, axiom,
73.85/11.28	  (all_of(^[X0]: in(X0,nat),
73.85/11.28	          ^[X0]:
73.85/11.28	            all_of(^[X1]: in(X1,nat),^[X1]: (d_29_ii(X0,X1) => iii(X1,X0)))))).
73.85/11.28	tff(zf_stmt_0, axiom,
73.85/11.28	  (![X4]:
73.85/11.28	     (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
73.85/11.28	      (![X6]:
73.85/11.28	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
73.85/11.28	          (d_29_ii(X4,X6) => n_some(diffprop(X4,X6)))))))).
73.85/11.28	tff('6', plain,
73.85/11.28	    ![X103, X104]:
73.85/11.28	      (~ is_of(X103, 
73.85/11.28	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
73.85/11.28	       |  n_some(diffprop(X104, X103))
73.85/11.28	       | ~ d_29_ii(X104, X103)
73.85/11.28	       | ~ is_of(X104, 
73.85/11.28	             (^[Y0 : $i]:
73.85/11.28	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_0])).
73.85/11.28	tff(def_n_is, axiom, n_is() = e_is(nat)).
73.85/11.28	tff('7', plain, n_is = e_is(nat),
73.85/11.28	    inference('simplify_rw_rule', [status(thm)], [def_n_is, '3'])).
73.85/11.28	tff('8', plain, n_is = e_is(nat), define([status(thm)])).
73.85/11.28	tff(n_ax4, axiom,
73.85/11.28	  (all_of(^[X0]: in(X0,nat),
73.85/11.28	          ^[X0]:
73.85/11.28	            all_of(^[X1]: in(X1,nat),
73.85/11.28	                   ^[X1]: (n_is(ordsucc(X0),ordsucc(X1)) => n_is(X0,X1)))))).
73.85/11.28	tff(zf_stmt_1, axiom,
73.85/11.28	  (![X4]:
73.85/11.28	     (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
73.85/11.28	      (![X6]:
73.85/11.28	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
73.85/11.28	          (e_is(d_Sep(omega,^[V_5]: (V_5 != emptyset)),ordsucc(X4),
73.85/11.28	                ordsucc(X6)) =>
73.85/11.28	           e_is(d_Sep(omega,^[V_6]: (V_6 != emptyset)),X4,X6))))))).
73.85/11.28	tff('9', plain,
73.85/11.28	    ![X16, X17]:
73.85/11.28	      (~ is_of(X16, 
73.85/11.28	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
73.85/11.28	       |  e_is(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), X17, X16)
73.85/11.28	       | ~ e_is(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), ordsucc(X17), 
73.85/11.28	             ordsucc(X16))
73.85/11.28	       | ~ is_of(X17, 
73.85/11.28	             (^[Y0 : $i]:
73.85/11.28	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_1])).
73.85/11.28	tff('10', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('11', plain,
73.85/11.28	    ![X16, X17]:
73.85/11.28	      (~ is_of(X16, 
73.85/11.28	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
73.85/11.28	       |  e_is(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), X17, X16)
73.85/11.28	       | ~ e_is(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), ordsucc(X17), 
73.85/11.28	             ordsucc(X16))
73.85/11.28	       | ~ is_of(X17, 
73.85/11.28	             (^[Y0 : $i]:
73.85/11.28	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_1])).
73.85/11.28	tff('12', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('13', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('14', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('15', plain,
73.85/11.28	    ![X103, X104]:
73.85/11.28	      (~ is_of(X103, '#l_lift10628')
73.85/11.28	       |  n_some(diffprop(X104, X103))
73.85/11.28	       | ~ d_29_ii(X104, X103)
73.85/11.28	       | ~ is_of(X104, '#l_lift10628')),
73.85/11.28	    inference('lambda_lifting', [status(thm)], ['6', '10', '12', '13', '14'])).
73.85/11.28	tff(def_lessis, axiom, lessis() = ^[X0,X1]: l_or(iii(X0,X1),n_is(X0,X1))).
73.85/11.28	tff(def_l_or, axiom, l_or() = ^[X0:$o]: imp(d_not(X0))).
73.85/11.28	tff(def_d_not, axiom, d_not() = ^[X0:$o]: imp(X0,$false)).
73.85/11.28	tff('16', plain, d_not = (^[X0:$o]: imp(X0,$false)),
73.85/11.28	    inference('simplify_rw_rule', [status(thm)], [def_d_not])).
73.85/11.28	tff('17', plain, d_not = (^[V_1:$o]: imp(V_1,$false)), define([status(thm)])).
73.85/11.28	tff('18', plain, l_or = (^[X0:$o]: imp(d_not(X0))),
73.85/11.28	    inference('simplify_rw_rule', [status(thm)], [def_l_or, '17'])).
73.85/11.28	tff('19', plain, l_or = (^[V_1:$o]: imp(d_not(V_1))), define([status(thm)])).
73.85/11.28	tff('20', plain, lessis = (^[X0,X1]: l_or(iii(X0,X1),n_is(X0,X1))),
73.85/11.28	    inference('simplify_rw_rule', [status(thm)],
73.85/11.28	              [def_lessis, '1', '8', '3', '19', '17'])).
73.85/11.28	tff('21', plain, lessis = (^[V_1,V_2]: l_or(iii(V_1,V_2),n_is(V_1,V_2))),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff(satz10k, axiom,
73.85/11.28	  (all_of(^[X0]: in(X0,nat),
73.85/11.28	          ^[X0]:
73.85/11.28	            all_of(^[X1]: in(X1,nat),
73.85/11.28	                   ^[X1]: (d_not(lessis(X0,X1)) => d_29_ii(X0,X1)))))).
73.85/11.28	tff(zf_stmt_2, axiom,
73.85/11.28	  (![X4]:
73.85/11.28	     (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
73.85/11.28	      (![X6]:
73.85/11.28	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
73.85/11.28	          (imp(imp(imp(n_some(diffprop(X6,X4)),$false),
73.85/11.28	                   e_is(d_Sep(omega,^[V_5]: (V_5 != emptyset)),X4,X6)),
73.85/11.28	               $false) =>
73.85/11.28	           d_29_ii(X4,X6))))))).
73.85/11.28	tff('22', plain,
73.85/11.28	    ![X74, X75]:
73.85/11.28	      (~ is_of(X74, 
73.85/11.28	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
73.85/11.28	       |  d_29_ii(X75, X74)
73.85/11.28	       | ~ imp(
73.85/11.28	             imp(imp(n_some(diffprop(X74, X75)), $false), 
73.85/11.28	               e_is(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), X75, X74)), 
73.85/11.28	             $false)
73.85/11.28	       | ~ is_of(X75, 
73.85/11.28	             (^[Y0 : $i]:
73.85/11.28	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_2])).
73.85/11.28	tff('23', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('24', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('25', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('26', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('27', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('28', plain,
73.85/11.28	    ![X74, X75]:
73.85/11.28	      (~ is_of(X74, '#l_lift10628')
73.85/11.28	       |  d_29_ii(X75, X74)
73.85/11.28	       | ~ imp(
73.85/11.28	             imp(imp(n_some(diffprop(X74, X75)), $false), 
73.85/11.28	               e_is(d_Sep(omega, '#l_lift10627'), X75, X74)), $false)
73.85/11.28	       | ~ is_of(X75, '#l_lift10628')),
73.85/11.28	    inference('lambda_lifting', [status(thm)],
73.85/11.28	              ['22', '23', '24', '25', '26', '27'])).
73.85/11.28	tff(def_n_pl, axiom, n_pl() = ^[X0]: ap(plus(X0))).
73.85/11.28	tff('29', plain, n_pl = (^[X0]: ap(plus(X0))),
73.85/11.28	    inference('simplify_rw_rule', [status(thm)], [def_n_pl])).
73.85/11.28	tff('30', plain, n_pl = (^[V_1]: ap(plus(V_1))), define([status(thm)])).
73.85/11.28	tff(satz19k, axiom,
73.85/11.28	  (all_of(^[X0]: in(X0,nat),
73.85/11.28	          ^[X0]:
73.85/11.28	            all_of(^[X1]: in(X1,nat),
73.85/11.28	                   ^[X1]:
73.85/11.28	                     all_of(^[X2]: in(X2,nat),
73.85/11.28	                            ^[X2]:
73.85/11.28	                              all_of(^[X3]: in(X3,nat),
73.85/11.28	                                     ^[X3]:
73.85/11.28	                                       (n_is(X0,X1) =>
73.85/11.28	                                        (iii(X2,X3) =>
73.85/11.28	                                         iii(n_pl(X2,X0),n_pl(X3,X1)))))))))).
73.85/11.28	tff(zf_stmt_3, axiom,
73.85/11.28	  (![X4]:
73.85/11.28	     (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
73.85/11.28	      (![X6]:
73.85/11.28	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
73.85/11.28	          (![X8]:
73.85/11.28	             (is_of(X8,^[V_5]: in(V_5,d_Sep(omega,^[V_6]: (V_6 != emptyset)))) =>
73.85/11.28	              (![X10]:
73.85/11.28	                 (is_of(X10,
73.85/11.28	                        ^[V_7]:
73.85/11.28	                          in(V_7,d_Sep(omega,^[V_8]: (V_8 != emptyset)))) =>
73.85/11.28	                  (e_is(d_Sep(omega,^[V_9]: (V_9 != emptyset)),X4,X6) =>
73.85/11.28	                   (n_some(diffprop(X10,X8)) =>
73.85/11.28	                    n_some(diffprop(ap(plus(X10),X6),ap(plus(X8),X4)))))))))))))).
73.85/11.28	tff('31', plain,
73.85/11.28	    ![X44, X45, X46, X47]:
73.85/11.28	      (~ is_of(X44, 
73.85/11.28	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
73.85/11.28	       | ~ is_of(X45, 
73.85/11.28	             (^[Y0 : $i]:
73.85/11.28	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
73.85/11.28	       | ~ n_some(diffprop(X45, X46))
73.85/11.28	       |  n_some(diffprop(ap(plus(X45), X44), ap(plus(X46), X47)))
73.85/11.28	       | ~ e_is(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), X47, X44)
73.85/11.28	       | ~ is_of(X46, 
73.85/11.28	             (^[Y0 : $i]:
73.85/11.28	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
73.85/11.28	       | ~ is_of(X47, 
73.85/11.28	             (^[Y0 : $i]:
73.85/11.28	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_3])).
73.85/11.28	tff('32', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('33', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('34', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('35', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('36', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('37', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('38', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('39', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('40', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('41', plain,
73.85/11.28	    ![X44, X45, X46, X47]:
73.85/11.28	      (~ is_of(X44, '#l_lift10628')
73.85/11.28	       | ~ is_of(X45, '#l_lift10628')
73.85/11.28	       | ~ n_some(diffprop(X45, X46))
73.85/11.28	       |  n_some(diffprop(ap(plus(X45), X44), ap(plus(X46), X47)))
73.85/11.28	       | ~ e_is(d_Sep(omega, '#l_lift10627'), X47, X44)
73.85/11.28	       | ~ is_of(X46, '#l_lift10628')
73.85/11.28	       | ~ is_of(X47, '#l_lift10628')),
73.85/11.28	    inference('lambda_lifting', [status(thm)],
73.85/11.28	              ['31', '32', '33', '34', '35', '36', '37', '38', '39', '40'])).
73.85/11.28	tff(satz22d, conjecture,
73.85/11.28	  (all_of(^[X0]: in(X0,nat),
73.85/11.28	          ^[X0]:
73.85/11.28	            all_of(^[X1]: in(X1,nat),
73.85/11.28	                   ^[X1]:
73.85/11.28	                     all_of(^[X2]: in(X2,nat),
73.85/11.28	                            ^[X2]:
73.85/11.28	                              all_of(^[X3]: in(X3,nat),
73.85/11.28	                                     ^[X3]:
73.85/11.28	                                       (iii(X0,X1) =>
73.85/11.28	                                        (lessis(X2,X3) =>
73.85/11.28	                                         iii(n_pl(X0,X2),n_pl(X1,X3)))))))))).
73.85/11.28	tff(zf_stmt_4, conjecture,
73.85/11.28	  (![X4]:
73.85/11.28	     (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
73.85/11.28	      (![X6]:
73.85/11.28	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
73.85/11.28	          (![X8]:
73.85/11.28	             (is_of(X8,^[V_5]: in(V_5,d_Sep(omega,^[V_6]: (V_6 != emptyset)))) =>
73.85/11.28	              (![X10]:
73.85/11.28	                 (is_of(X10,
73.85/11.28	                        ^[V_7]:
73.85/11.28	                          in(V_7,d_Sep(omega,^[V_8]: (V_8 != emptyset)))) =>
73.85/11.28	                  (n_some(diffprop(X6,X4)) =>
73.85/11.28	                   (imp(imp(n_some(diffprop(X10,X8)),$false),
73.85/11.28	                        e_is(d_Sep(omega,^[V_9]: (V_9 != emptyset)),X8,X10)) =>
73.85/11.28	                    n_some(diffprop(ap(plus(X6),X10),ap(plus(X4),X8)))))))))))))).
73.85/11.28	tff(zf_stmt_5, negated_conjecture,
73.85/11.28	  (~
73.85/11.28	    (![X4]:
73.85/11.28	       (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
73.85/11.28	        (![X6]:
73.85/11.28	           (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
73.85/11.28	            (![X8]:
73.85/11.28	               (is_of(X8,
73.85/11.28	                      ^[V_5]: in(V_5,d_Sep(omega,^[V_6]: (V_6 != emptyset)))) =>
73.85/11.28	                (![X10]:
73.85/11.28	                   (is_of(X10,
73.85/11.28	                          ^[V_7]:
73.85/11.28	                            in(V_7,d_Sep(omega,^[V_8]: (V_8 != emptyset)))) =>
73.85/11.28	                    (n_some(diffprop(X6,X4)) =>
73.85/11.28	                     (imp(imp(n_some(diffprop(X10,X8)),$false),
73.85/11.28	                          e_is(d_Sep(omega,^[V_9]: (V_9 != emptyset)),X8,X10)) =>
73.85/11.28	                      n_some(diffprop(ap(plus(X6),X10),ap(plus(X4),X8))))))))))))))).
73.85/11.28	tff('42', plain,
73.85/11.28	     is_of(sk_X6, 
73.85/11.28	       (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_5])).
73.85/11.28	tff('43', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('44', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('45', plain,  is_of(sk_X6, '#l_lift10628'),
73.85/11.28	    inference('lambda_lifting', [status(thm)], ['42', '43', '44'])).
73.85/11.28	tff('46', plain,
73.85/11.28	     is_of(sk_X10, 
73.85/11.28	       (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_5])).
73.85/11.28	tff('47', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('48', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('49', plain,  is_of(sk_X10, '#l_lift10628'),
73.85/11.28	    inference('lambda_lifting', [status(thm)], ['46', '47', '48'])).
73.85/11.28	tff('50', plain,
73.85/11.28	     is_of(sk_X8, 
73.85/11.28	       (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_5])).
73.85/11.28	tff('51', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('52', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('53', plain,  is_of(sk_X8, '#l_lift10628'),
73.85/11.28	    inference('lambda_lifting', [status(thm)], ['50', '51', '52'])).
73.85/11.28	tff('54', plain,
73.85/11.28	     is_of(sk_X4, 
73.85/11.28	       (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset)))))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_5])).
73.85/11.28	tff('55', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('56', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('57', plain,  is_of(sk_X4, '#l_lift10628'),
73.85/11.28	    inference('lambda_lifting', [status(thm)], ['54', '55', '56'])).
73.85/11.28	tff('58', plain,  n_some(diffprop(sk_X6, sk_X4)),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_5])).
73.85/11.28	tff(satz21a, axiom,
73.85/11.28	  (all_of(^[X0]: in(X0,nat),
73.85/11.28	          ^[X0]:
73.85/11.28	            all_of(^[X1]: in(X1,nat),
73.85/11.28	                   ^[X1]:
73.85/11.28	                     all_of(^[X2]: in(X2,nat),
73.85/11.28	                            ^[X2]:
73.85/11.28	                              all_of(^[X3]: in(X3,nat),
73.85/11.28	                                     ^[X3]:
73.85/11.28	                                       (iii(X0,X1) =>
73.85/11.28	                                        (iii(X2,X3) =>
73.85/11.28	                                         iii(n_pl(X0,X2),n_pl(X1,X3)))))))))).
73.85/11.28	tff(zf_stmt_6, axiom,
73.85/11.28	  (![X4]:
73.85/11.28	     (is_of(X4,^[V_1]: in(V_1,d_Sep(omega,^[V_2]: (V_2 != emptyset)))) =>
73.85/11.28	      (![X6]:
73.85/11.28	         (is_of(X6,^[V_3]: in(V_3,d_Sep(omega,^[V_4]: (V_4 != emptyset)))) =>
73.85/11.28	          (![X8]:
73.85/11.28	             (is_of(X8,^[V_5]: in(V_5,d_Sep(omega,^[V_6]: (V_6 != emptyset)))) =>
73.85/11.28	              (![X10]:
73.85/11.28	                 (is_of(X10,
73.85/11.28	                        ^[V_7]:
73.85/11.28	                          in(V_7,d_Sep(omega,^[V_8]: (V_8 != emptyset)))) =>
73.85/11.28	                  (n_some(diffprop(X6,X4)) =>
73.85/11.28	                   (n_some(diffprop(X10,X8)) =>
73.85/11.28	                    n_some(diffprop(ap(plus(X6),X10),ap(plus(X4),X8)))))))))))))).
73.85/11.28	tff('59', plain,
73.85/11.28	    ![X132, X133, X134, X135]:
73.85/11.28	      (~ is_of(X132, 
73.85/11.28	           (^[Y0 : $i]: in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
73.85/11.28	       | ~ is_of(X133, 
73.85/11.28	             (^[Y0 : $i]:
73.85/11.28	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
73.85/11.28	       | ~ n_some(diffprop(X133, X134))
73.85/11.28	       |  n_some(diffprop(ap(plus(X132), X133), ap(plus(X135), X134)))
73.85/11.28	       | ~ n_some(diffprop(X132, X135))
73.85/11.28	       | ~ is_of(X134, 
73.85/11.28	             (^[Y0 : $i]:
73.85/11.28	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))
73.85/11.28	       | ~ is_of(X135, 
73.85/11.28	             (^[Y0 : $i]:
73.85/11.28	                in(Y0, d_Sep(omega, (^[Y1 : $i]: (Y1 != emptyset))))))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_6])).
73.85/11.28	tff('60', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('61', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('62', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('63', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('64', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('65', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('66', plain,
73.85/11.28	    ![X19]: '#l_lift10628'(X19) = in(X19, d_Sep(omega, '#l_lift10627')),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('67', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('68', plain,
73.85/11.28	    ![X132, X133, X134, X135]:
73.85/11.28	      (~ is_of(X132, '#l_lift10628')
73.85/11.28	       | ~ is_of(X133, '#l_lift10628')
73.85/11.28	       | ~ n_some(diffprop(X133, X134))
73.85/11.28	       |  n_some(diffprop(ap(plus(X132), X133), ap(plus(X135), X134)))
73.85/11.28	       | ~ n_some(diffprop(X132, X135))
73.85/11.28	       | ~ is_of(X134, '#l_lift10628')
73.85/11.28	       | ~ is_of(X135, '#l_lift10628')),
73.85/11.28	    inference('lambda_lifting', [status(thm)],
73.85/11.28	              ['59', '60', '61', '62', '63', '64', '65', '66', '67'])).
73.85/11.28	tff('69', plain,
73.85/11.28	    ~ n_some(diffprop(ap(plus(sk_X6), sk_X10), ap(plus(sk_X4), sk_X8))),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_5])).
73.85/11.28	tff('70', plain,
73.85/11.28	     imp(imp(n_some(diffprop(sk_X10, sk_X8)), $false), 
73.85/11.28	       e_is(d_Sep(omega, (^[Y0 : $i]: (Y0 != emptyset))), sk_X8, sk_X10)),
73.85/11.28	    inference('cnf', [status(esa)], [zf_stmt_5])).
73.85/11.28	tff('71', plain, ![X18]: '#l_lift10627'(X18) = (X18 != emptyset),
73.85/11.28	    define([status(thm)])).
73.85/11.28	tff('72', plain,
73.85/11.28	     imp(imp(n_some(diffprop(sk_X10, sk_X8)), $false), 
73.85/11.28	       e_is(d_Sep(omega, '#l_lift10627'), sk_X8, sk_X10)),
73.85/11.28	    inference('lambda_lifting', [status(thm)], ['70', '71'])).
73.85/11.28	tff('73', plain, $false,
73.85/11.28	    inference('eprover', [status(thm)],
73.85/11.28	              ['15', '28', '41', '45', '49', '53', '57', '58', '68', '69', 
73.85/11.28	               '72'])).
73.85/11.28	
73.85/11.28	% SZS output end Refutation
73.85/11.28	
73.85/11.28	
73.85/11.28	% Terminating...
73.85/11.34	% Runner terminated.
74.61/11.35	% Zipperpin 1.5 exiting
74.61/11.36	EOF