%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:44:32 EDT 2023

% Result   : Theorem 0.30s 1.37s
% Output   : Proof 0.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.11  % Command  : nanocop.sh %s %d
% 0.11/0.32  % Computer : n027.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May 18 17:06:20 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.30/1.37  
% 0.30/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.30/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/1.37  %-----------------------------------------------------
% 0.30/1.37  ncf(matrix, plain, [(571 ^ _72436) ^ [] : [-(relation(569 ^ []))], (573 ^ _72436) ^ [] : [-(function(569 ^ []))], (575 ^ _72436) ^ [] : [-(ordinal(relation_dom(569 ^ [])))], (577 ^ _72436) ^ [] : [transfinite_sequence_of(569 ^ [], relation_rng(569 ^ []))], (186 ^ _72436) ^ [_78239, _78241] : [_78241 = _78239, -(powerset(_78241) = powerset(_78239))], (192 ^ _72436) ^ [_78457, _78459] : [_78459 = _78457, -(relation_dom(_78459) = relation_dom(_78457))], (198 ^ _72436) ^ [_78655, _78657] : [_78657 = _78655, -(relation_rng(_78657) = relation_rng(_78655))], (2 ^ _72436) ^ [_72580] : [-(_72580 = _72580)], (4 ^ _72436) ^ [_72687, _72689] : [_72689 = _72687, -(_72687 = _72689)], (10 ^ _72436) ^ [_72891, _72893, _72895] : [-(_72895 = _72891), _72895 = _72893, _72893 = _72891], (20 ^ _72436) ^ [_73204, _73206] : [-(with_non_empty_elements(_73204)), _73206 = _73204, with_non_empty_elements(_73206)], (30 ^ _72436) ^ [_73499, _73501] : [-(one_to_one(_73499)), _73501 = _73499, one_to_one(_73501)], (40 ^ _72436) ^ [_73794, _73796] : [-(epsilon_transitive(_73794)), _73796 = _73794, epsilon_transitive(_73796)], (50 ^ _72436) ^ [_74089, _74091] : [-(epsilon_connected(_74089)), _74091 = _74089, epsilon_connected(_74091)], (60 ^ _72436) ^ [_74384, _74386] : [-(relation_empty_yielding(_74384)), _74386 = _74384, relation_empty_yielding(_74386)], (70 ^ _72436) ^ [_74679, _74681] : [-(transfinite_sequence(_74679)), _74681 = _74679, transfinite_sequence(_74681)], (80 ^ _72436) ^ [_74974, _74976] : [-(relation_non_empty(_74974)), _74976 = _74974, relation_non_empty(_74976)], (90 ^ _72436) ^ [_75297, _75299, _75301, _75303] : [-(subset(_75301, _75297)), subset(_75303, _75299), _75303 = _75301, _75299 = _75297], (104 ^ _72436) ^ [_75741, _75743, _75745, _75747] : [-(element(_75745, _75741)), element(_75747, _75743), _75747 = _75745, _75743 = _75741], (118 ^ _72436) ^ [_76185, _76187, _76189, _76191] : [-(in(_76189, _76185)), in(_76191, _76187), _76191 = _76189, _76187 = _76185], (132 ^ _72436) ^ [_76601, _76603] : [-(empty(_76601)), _76603 = _76601, empty(_76603)], (142 ^ _72436) ^ [_76896, _76898] : [-(relation(_76896)), _76898 = _76896, relation(_76898)], (152 ^ _72436) ^ [_77191, _77193] : [-(function(_77191)), _77193 = _77191, function(_77193)], (162 ^ _72436) ^ [_77486, _77488] : [-(ordinal(_77486)), _77488 = _77486, ordinal(_77488)], (172 ^ _72436) ^ [_77789, _77791, _77793, _77795] : [-(transfinite_sequence_of(_77793, _77789)), transfinite_sequence_of(_77795, _77791), _77795 = _77793, _77791 = _77789], (204 ^ _72436) ^ [_78915, _78917] : [in(_78917, _78915), in(_78915, _78917)], (210 ^ _72436) ^ [_79112] : [empty(_79112), -(function(_79112))], (216 ^ _72436) ^ [_79298] : [ordinal(_79298), 219 ^ _72436 : [(220 ^ _72436) ^ [] : [-(epsilon_transitive(_79298))], (222 ^ _72436) ^ [] : [-(epsilon_connected(_79298))]]], (224 ^ _72436) ^ [_79555] : [empty(_79555), -(relation(_79555))], (230 ^ _72436) ^ [_79741] : [241 ^ _72436 : [(242 ^ _72436) ^ [] : [-(relation(_79741))], (244 ^ _72436) ^ [] : [-(function(_79741))], (246 ^ _72436) ^ [] : [-(one_to_one(_79741))]], relation(_79741), empty(_79741), function(_79741)], (248 ^ _72436) ^ [_80234] : [-(ordinal(_80234)), epsilon_transitive(_80234), epsilon_connected(_80234)], (258 ^ _72436) ^ [_80503] : [empty(_80503), 261 ^ _72436 : [(262 ^ _72436) ^ [] : [-(epsilon_transitive(_80503))], (264 ^ _72436) ^ [] : [-(epsilon_connected(_80503))], (266 ^ _72436) ^ [] : [-(ordinal(_80503))]]], (268 ^ _72436) ^ [_80830] : [relation(_80830), function(_80830), 275 ^ _72436 : [(276 ^ _72436) ^ [] : [transfinite_sequence(_80830), -(ordinal(relation_dom(_80830)))], (282 ^ _72436) ^ [] : [ordinal(relation_dom(_80830)), -(transfinite_sequence(_80830))]]], (288 ^ _72436) ^ [_81357, _81359] : [relation(_81357), function(_81357), transfinite_sequence(_81357), 299 ^ _72436 : [(300 ^ _72436) ^ [] : [transfinite_sequence_of(_81357, _81359), -(subset(relation_rng(_81357), _81359))], (306 ^ _72436) ^ [] : [subset(relation_rng(_81357), _81359), -(transfinite_sequence_of(_81357, _81359))]]], (312 ^ _72436) ^ [_81999, _82001] : [transfinite_sequence_of(_81999, _82001), 315 ^ _72436 : [(316 ^ _72436) ^ [] : [-(relation(_81999))], (318 ^ _72436) ^ [] : [-(function(_81999))], (320 ^ _72436) ^ [] : [-(transfinite_sequence(_81999))]]], (323 ^ _72436) ^ [_82362] : [-(transfinite_sequence_of(321 ^ [_82362], _82362))], (326 ^ _72436) ^ [_82484] : [-(element(324 ^ [_82484], _82484))], (328 ^ _72436) ^ [] : [-(empty(empty_set))], (330 ^ _72436) ^ [] : [-(relation(empty_set))], (332 ^ _72436) ^ [] : [-(relation_empty_yielding(empty_set))], (334 ^ _72436) ^ [] : [-(empty(empty_set))], (336 ^ _72436) ^ [] : [-(relation(empty_set))], (338 ^ _72436) ^ [] : [-(relation_empty_yielding(empty_set))], (340 ^ _72436) ^ [] : [-(function(empty_set))], (342 ^ _72436) ^ [] : [-(one_to_one(empty_set))], (344 ^ _72436) ^ [] : [-(empty(empty_set))], (346 ^ _72436) ^ [] : [-(epsilon_transitive(empty_set))], (348 ^ _72436) ^ [] : [-(epsilon_connected(empty_set))], (350 ^ _72436) ^ [] : [-(ordinal(empty_set))], (352 ^ _72436) ^ [] : [-(empty(empty_set))], (354 ^ _72436) ^ [] : [-(relation(empty_set))], (356 ^ _72436) ^ [_83344] : [empty(relation_dom(_83344)), -(empty(_83344)), relation(_83344)], (366 ^ _72436) ^ [_83621] : [-(with_non_empty_elements(relation_rng(_83621))), relation(_83621), relation_non_empty(_83621), function(_83621)], (380 ^ _72436) ^ [_83977] : [empty(relation_rng(_83977)), -(empty(_83977)), relation(_83977)], (390 ^ _72436) ^ [_84254] : [empty(_84254), 393 ^ _72436 : [(394 ^ _72436) ^ [] : [-(empty(relation_dom(_84254)))], (396 ^ _72436) ^ [] : [-(relation(relation_dom(_84254)))]]], (398 ^ _72436) ^ [_84519] : [empty(_84519), 401 ^ _72436 : [(402 ^ _72436) ^ [] : [-(empty(relation_rng(_84519)))], (404 ^ _72436) ^ [] : [-(relation(relation_rng(_84519)))]]], (407 ^ _72436) ^ [] : [-(relation(405 ^ []))], (409 ^ _72436) ^ [] : [-(function(405 ^ []))], (412 ^ _72436) ^ [] : [-(epsilon_transitive(410 ^ []))], (414 ^ _72436) ^ [] : [-(epsilon_connected(410 ^ []))], (416 ^ _72436) ^ [] : [-(ordinal(410 ^ []))], (419 ^ _72436) ^ [] : [-(empty(417 ^ []))], (421 ^ _72436) ^ [] : [-(relation(417 ^ []))], (424 ^ _72436) ^ [] : [-(empty(422 ^ []))], (427 ^ _72436) ^ [] : [-(relation(425 ^ []))], (429 ^ _72436) ^ [] : [-(empty(425 ^ []))], (431 ^ _72436) ^ [] : [-(function(425 ^ []))], (434 ^ _72436) ^ [] : [-(relation(432 ^ []))], (436 ^ _72436) ^ [] : [-(function(432 ^ []))], (438 ^ _72436) ^ [] : [-(one_to_one(432 ^ []))], (440 ^ _72436) ^ [] : [-(empty(432 ^ []))], (442 ^ _72436) ^ [] : [-(epsilon_transitive(432 ^ []))], (444 ^ _72436) ^ [] : [-(epsilon_connected(432 ^ []))], (446 ^ _72436) ^ [] : [-(ordinal(432 ^ []))], (449 ^ _72436) ^ [] : [empty(447 ^ [])], (451 ^ _72436) ^ [] : [-(relation(447 ^ []))], (454 ^ _72436) ^ [] : [empty(452 ^ [])], (457 ^ _72436) ^ [] : [-(relation(455 ^ []))], (459 ^ _72436) ^ [] : [-(function(455 ^ []))], (461 ^ _72436) ^ [] : [-(one_to_one(455 ^ []))], (464 ^ _72436) ^ [] : [empty(462 ^ [])], (466 ^ _72436) ^ [] : [-(epsilon_transitive(462 ^ []))], (468 ^ _72436) ^ [] : [-(epsilon_connected(462 ^ []))], (470 ^ _72436) ^ [] : [-(ordinal(462 ^ []))], (473 ^ _72436) ^ [] : [-(relation(471 ^ []))], (475 ^ _72436) ^ [] : [-(relation_empty_yielding(471 ^ []))], (478 ^ _72436) ^ [] : [-(relation(476 ^ []))], (480 ^ _72436) ^ [] : [-(relation_empty_yielding(476 ^ []))], (482 ^ _72436) ^ [] : [-(function(476 ^ []))], (485 ^ _72436) ^ [] : [-(relation(483 ^ []))], (487 ^ _72436) ^ [] : [-(function(483 ^ []))], (489 ^ _72436) ^ [] : [-(transfinite_sequence(483 ^ []))], (492 ^ _72436) ^ [] : [-(relation(490 ^ []))], (494 ^ _72436) ^ [] : [-(relation_non_empty(490 ^ []))], (496 ^ _72436) ^ [] : [-(function(490 ^ []))], (498 ^ _72436) ^ [_87532, _87534] : [-(subset(_87534, _87534))], (500 ^ _72436) ^ [_87641, _87643] : [in(_87643, _87641), -(element(_87643, _87641))], (506 ^ _72436) ^ [_87851, _87853] : [element(_87853, _87851), -(empty(_87851)), -(in(_87853, _87851))], (516 ^ _72436) ^ [_88178, _88180] : [element(_88180, powerset(_88178)), -(subset(_88180, _88178))], (522 ^ _72436) ^ [_88344, _88346] : [subset(_88346, _88344), -(element(_88346, powerset(_88344)))], (528 ^ _72436) ^ [_88574, _88576, _88578] : [-(element(_88578, _88574)), in(_88578, _88576), element(_88576, powerset(_88574))], (538 ^ _72436) ^ [_88901, _88903, _88905] : [in(_88905, _88903), element(_88903, powerset(_88901)), empty(_88901)], (548 ^ _72436) ^ [_89197] : [empty(_89197), -(_89197 = empty_set)], (554 ^ _72436) ^ [_89399, _89401] : [in(_89401, _89399), empty(_89399)], (560 ^ _72436) ^ [_89586, _89588] : [empty(_89588), -(_89588 = _89586), empty(_89586)]], input).
% 0.30/1.37  ncf('1',plain,[transfinite_sequence_of(569 ^ [], relation_rng(569 ^ []))],start(577 ^ 0)).
% 0.30/1.37  ncf('1.1',plain,[-(transfinite_sequence_of(569 ^ [], relation_rng(569 ^ []))), 306 : subset(relation_rng(569 ^ []), relation_rng(569 ^ [])), 306 : relation(569 ^ []), 306 : function(569 ^ []), 306 : transfinite_sequence(569 ^ [])],extension(288 ^ 1,bind([[_81357, _81359], [569 ^ [], relation_rng(569 ^ [])]]))).
% 0.30/1.37  ncf('1.1.1',plain,[-(subset(relation_rng(569 ^ []), relation_rng(569 ^ [])))],extension(498 ^ 4,bind([[_87532, _87534], [_53344, relation_rng(569 ^ [])]]))).
% 0.30/1.37  ncf('1.1.2',plain,[-(relation(569 ^ []))],extension(571 ^ 2)).
% 0.30/1.37  ncf('1.1.3',plain,[-(function(569 ^ []))],extension(573 ^ 2)).
% 0.30/1.37  ncf('1.1.4',plain,[-(transfinite_sequence(569 ^ [])), 282 : ordinal(relation_dom(569 ^ [])), 282 : relation(569 ^ []), 282 : function(569 ^ [])],extension(268 ^ 2,bind([[_80830], [569 ^ []]]))).
% 0.30/1.37  ncf('1.1.4.1',plain,[-(ordinal(relation_dom(569 ^ [])))],extension(575 ^ 5)).
% 0.30/1.37  ncf('1.1.4.2',plain,[-(relation(569 ^ []))],lemmata('[1].x')).
% 0.30/1.37  ncf('1.1.4.3',plain,[-(function(569 ^ []))],lemmata('[1].x')).
% 0.30/1.37  %-----------------------------------------------------
% 0.30/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------