%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL544+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n017.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 11:33:27 EDT 2023

% Result   : Theorem 18.25s 17.97s
% Output   : Proof 18.25s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL544+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 15:33:45 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 18.25/17.97  
% 18.25/17.97  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 18.25/17.97  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.25/17.97  %-----------------------------------------------------
% 18.25/17.97  ncf(matrix, plain, [(958 ^ _109033) ^ [] : [axiom_m4], (20 ^ _109033) ^ [_109781, _109783] : [-(is_a_theorem(_109781)), _109783 = _109781, is_a_theorem(_109783)], (2 ^ _109033) ^ [_109177] : [-(_109177 = _109177)], (4 ^ _109033) ^ [_109284, _109286] : [_109286 = _109284, -(_109284 = _109286)], (10 ^ _109033) ^ [_109488, _109490, _109492] : [-(_109492 = _109488), _109492 = _109490, _109490 = _109488], (30 ^ _109033) ^ [_110106, _110108, _110110, _110112] : [-(or(_110112, _110108) = or(_110110, _110106)), _110112 = _110110, _110108 = _110106], (40 ^ _109033) ^ [_110465, _110467, _110469, _110471] : [-(equiv(_110471, _110467) = equiv(_110469, _110465)), _110471 = _110469, _110467 = _110465], (50 ^ _109033) ^ [_110796, _110798] : [_110798 = _110796, -(possibly(_110798) = possibly(_110796))], (56 ^ _109033) ^ [_111014, _111016] : [_111016 = _111014, -((not _111016) = (not _111014))], (62 ^ _109033) ^ [_111232, _111234] : [_111234 = _111232, -(necessarily(_111234) = necessarily(_111232))], (68 ^ _109033) ^ [_111478, _111480, _111482, _111484] : [-(implies(_111484, _111480) = implies(_111482, _111478)), _111484 = _111482, _111480 = _111478], (78 ^ _109033) ^ [_111837, _111839, _111841, _111843] : [-(strict_equiv(_111843, _111839) = strict_equiv(_111841, _111837)), _111843 = _111841, _111839 = _111837], (88 ^ _109033) ^ [_112196, _112198, _112200, _112202] : [-(and(_112202, _112198) = and(_112200, _112196)), _112202 = _112200, _112198 = _112196], (98 ^ _109033) ^ [_112535, _112537, _112539, _112541] : [-(strict_implies(_112541, _112537) = strict_implies(_112539, _112535)), _112541 = _112539, _112537 = _112535], (122 ^ _109033) ^ [] : [125 ^ _109033 : [(126 ^ _109033) ^ [] : [-(is_a_theorem(123 ^ []))], (128 ^ _109033) ^ [] : [-(is_a_theorem(implies(123 ^ [], 124 ^ [])))], (130 ^ _109033) ^ [] : [is_a_theorem(124 ^ [])]], -(modus_ponens)], (108 ^ _109033) ^ [] : [modus_ponens, 111 ^ _109033 : [(112 ^ _109033) ^ [_113001, _113003] : [-(is_a_theorem(_113001)), is_a_theorem(_113003), is_a_theorem(implies(_113003, _113001))]]], (144 ^ _109033) ^ [] : [147 ^ _109033 : [(148 ^ _109033) ^ [] : [-(is_a_theorem(equiv(145 ^ [], 146 ^ [])))], (150 ^ _109033) ^ [] : [145 ^ [] = 146 ^ []]], -(substitution_of_equivalents)], (134 ^ _109033) ^ [] : [substitution_of_equivalents, 137 ^ _109033 : [(138 ^ _109033) ^ [_113711, _113713] : [is_a_theorem(equiv(_113713, _113711)), -(_113713 = _113711)]]], (154 ^ _109033) ^ [] : [modus_tollens, 157 ^ _109033 : [(158 ^ _109033) ^ [_114258, _114260] : [-(is_a_theorem(implies(implies(not _114258, not _114260), implies(_114260, _114258))))]]], (160 ^ _109033) ^ [] : [is_a_theorem(implies(implies(not 162 ^ [], not 161 ^ []), implies(161 ^ [], 162 ^ []))), -(modus_tollens)], (168 ^ _109033) ^ [] : [implies_1, 171 ^ _109033 : [(172 ^ _109033) ^ [_114662, _114664] : [-(is_a_theorem(implies(_114664, implies(_114662, _114664))))]]], (174 ^ _109033) ^ [] : [is_a_theorem(implies(175 ^ [], implies(176 ^ [], 175 ^ []))), -(implies_1)], (182 ^ _109033) ^ [] : [implies_2, 185 ^ _109033 : [(186 ^ _109033) ^ [_115047, _115049] : [-(is_a_theorem(implies(implies(_115049, implies(_115049, _115047)), implies(_115049, _115047))))]]], (188 ^ _109033) ^ [] : [is_a_theorem(implies(implies(189 ^ [], implies(189 ^ [], 190 ^ [])), implies(189 ^ [], 190 ^ []))), -(implies_2)], (196 ^ _109033) ^ [] : [implies_3, 199 ^ _109033 : [(200 ^ _109033) ^ [_115464, _115466, _115468] : [-(is_a_theorem(implies(implies(_115468, _115466), implies(implies(_115466, _115464), implies(_115468, _115464)))))]]], (202 ^ _109033) ^ [] : [is_a_theorem(implies(implies(203 ^ [], 204 ^ []), implies(implies(204 ^ [], 205 ^ []), implies(203 ^ [], 205 ^ [])))), -(implies_3)], (211 ^ _109033) ^ [] : [and_1, 214 ^ _109033 : [(215 ^ _109033) ^ [_115936, _115938] : [-(is_a_theorem(implies(and(_115938, _115936), _115938)))]]], (217 ^ _109033) ^ [] : [is_a_theorem(implies(and(218 ^ [], 219 ^ []), 218 ^ [])), -(and_1)], (225 ^ _109033) ^ [] : [and_2, 228 ^ _109033 : [(229 ^ _109033) ^ [_116321, _116323] : [-(is_a_theorem(implies(and(_116323, _116321), _116321)))]]], (231 ^ _109033) ^ [] : [is_a_theorem(implies(and(232 ^ [], 233 ^ []), 233 ^ [])), -(and_2)], (239 ^ _109033) ^ [] : [and_3, 242 ^ _109033 : [(243 ^ _109033) ^ [_116706, _116708] : [-(is_a_theorem(implies(_116708, implies(_116706, and(_116708, _116706)))))]]], (245 ^ _109033) ^ [] : [is_a_theorem(implies(246 ^ [], implies(247 ^ [], and(246 ^ [], 247 ^ [])))), -(and_3)], (253 ^ _109033) ^ [] : [or_1, 256 ^ _109033 : [(257 ^ _109033) ^ [_117100, _117102] : [-(is_a_theorem(implies(_117102, or(_117102, _117100))))]]], (259 ^ _109033) ^ [] : [is_a_theorem(implies(260 ^ [], or(260 ^ [], 261 ^ []))), -(or_1)], (267 ^ _109033) ^ [] : [or_2, 270 ^ _109033 : [(271 ^ _109033) ^ [_117485, _117487] : [-(is_a_theorem(implies(_117485, or(_117487, _117485))))]]], (273 ^ _109033) ^ [] : [is_a_theorem(implies(275 ^ [], or(274 ^ [], 275 ^ []))), -(or_2)], (281 ^ _109033) ^ [] : [or_3, 284 ^ _109033 : [(285 ^ _109033) ^ [_117884, _117886, _117888] : [-(is_a_theorem(implies(implies(_117888, _117884), implies(implies(_117886, _117884), implies(or(_117888, _117886), _117884)))))]]], (287 ^ _109033) ^ [] : [is_a_theorem(implies(implies(288 ^ [], 290 ^ []), implies(implies(289 ^ [], 290 ^ []), implies(or(288 ^ [], 289 ^ []), 290 ^ [])))), -(or_3)], (296 ^ _109033) ^ [] : [equivalence_1, 299 ^ _109033 : [(300 ^ _109033) ^ [_118368, _118370] : [-(is_a_theorem(implies(equiv(_118370, _118368), implies(_118370, _118368))))]]], (302 ^ _109033) ^ [] : [is_a_theorem(implies(equiv(303 ^ [], 304 ^ []), implies(303 ^ [], 304 ^ []))), -(equivalence_1)], (310 ^ _109033) ^ [] : [equivalence_2, 313 ^ _109033 : [(314 ^ _109033) ^ [_118762, _118764] : [-(is_a_theorem(implies(equiv(_118764, _118762), implies(_118762, _118764))))]]], (316 ^ _109033) ^ [] : [is_a_theorem(implies(equiv(317 ^ [], 318 ^ []), implies(318 ^ [], 317 ^ []))), -(equivalence_2)], (324 ^ _109033) ^ [] : [equivalence_3, 327 ^ _109033 : [(328 ^ _109033) ^ [_119156, _119158] : [-(is_a_theorem(implies(implies(_119158, _119156), implies(implies(_119156, _119158), equiv(_119158, _119156)))))]]], (330 ^ _109033) ^ [] : [is_a_theorem(implies(implies(331 ^ [], 332 ^ []), implies(implies(332 ^ [], 331 ^ []), equiv(331 ^ [], 332 ^ [])))), -(equivalence_3)], (338 ^ _109033) ^ [] : [kn1, 341 ^ _109033 : [(342 ^ _109033) ^ [_119554] : [-(is_a_theorem(implies(_119554, and(_119554, _119554))))]]], (344 ^ _109033) ^ [] : [is_a_theorem(implies(345 ^ [], and(345 ^ [], 345 ^ []))), -(kn1)], (351 ^ _109033) ^ [] : [kn2, 354 ^ _109033 : [(355 ^ _109033) ^ [_119890, _119892] : [-(is_a_theorem(implies(and(_119892, _119890), _119892)))]]], (357 ^ _109033) ^ [] : [is_a_theorem(implies(and(358 ^ [], 359 ^ []), 358 ^ [])), -(kn2)], (365 ^ _109033) ^ [] : [kn3, 368 ^ _109033 : [(369 ^ _109033) ^ [_120289, _120291, _120293] : [-(is_a_theorem(implies(implies(_120293, _120291), implies(not and(_120291, _120289), not and(_120289, _120293)))))]]], (371 ^ _109033) ^ [] : [is_a_theorem(implies(implies(372 ^ [], 373 ^ []), implies(not and(373 ^ [], 374 ^ []), not and(374 ^ [], 372 ^ [])))), -(kn3)], (380 ^ _109033) ^ [] : [cn1, 383 ^ _109033 : [(384 ^ _109033) ^ [_120791, _120793, _120795] : [-(is_a_theorem(implies(implies(_120795, _120793), implies(implies(_120793, _120791), implies(_120795, _120791)))))]]], (386 ^ _109033) ^ [] : [is_a_theorem(implies(implies(387 ^ [], 388 ^ []), implies(implies(388 ^ [], 389 ^ []), implies(387 ^ [], 389 ^ [])))), -(cn1)], (395 ^ _109033) ^ [] : [cn2, 398 ^ _109033 : [(399 ^ _109033) ^ [_121263, _121265] : [-(is_a_theorem(implies(_121265, implies(not _121265, _121263))))]]], (401 ^ _109033) ^ [] : [is_a_theorem(implies(402 ^ [], implies(not 402 ^ [], 403 ^ []))), -(cn2)], (409 ^ _109033) ^ [] : [cn3, 412 ^ _109033 : [(413 ^ _109033) ^ [_121638] : [-(is_a_theorem(implies(implies(not _121638, _121638), _121638)))]]], (415 ^ _109033) ^ [] : [is_a_theorem(implies(implies(not 416 ^ [], 416 ^ []), 416 ^ [])), -(cn3)], (422 ^ _109033) ^ [] : [r1, 425 ^ _109033 : [(426 ^ _109033) ^ [_121964] : [-(is_a_theorem(implies(or(_121964, _121964), _121964)))]]], (428 ^ _109033) ^ [] : [is_a_theorem(implies(or(429 ^ [], 429 ^ []), 429 ^ [])), -(r1)], (435 ^ _109033) ^ [] : [r2, 438 ^ _109033 : [(439 ^ _109033) ^ [_122300, _122302] : [-(is_a_theorem(implies(_122300, or(_122302, _122300))))]]], (441 ^ _109033) ^ [] : [is_a_theorem(implies(443 ^ [], or(442 ^ [], 443 ^ []))), -(r2)], (449 ^ _109033) ^ [] : [r3, 452 ^ _109033 : [(453 ^ _109033) ^ [_122685, _122687] : [-(is_a_theorem(implies(or(_122687, _122685), or(_122685, _122687))))]]], (455 ^ _109033) ^ [] : [is_a_theorem(implies(or(456 ^ [], 457 ^ []), or(457 ^ [], 456 ^ []))), -(r3)], (463 ^ _109033) ^ [] : [r4, 466 ^ _109033 : [(467 ^ _109033) ^ [_123093, _123095, _123097] : [-(is_a_theorem(implies(or(_123097, or(_123095, _123093)), or(_123095, or(_123097, _123093)))))]]], (469 ^ _109033) ^ [] : [is_a_theorem(implies(or(470 ^ [], or(471 ^ [], 472 ^ [])), or(471 ^ [], or(470 ^ [], 472 ^ [])))), -(r4)], (478 ^ _109033) ^ [] : [r5, 481 ^ _109033 : [(482 ^ _109033) ^ [_123562, _123564, _123566] : [-(is_a_theorem(implies(implies(_123564, _123562), implies(or(_123566, _123564), or(_123566, _123562)))))]]], (484 ^ _109033) ^ [] : [is_a_theorem(implies(implies(486 ^ [], 487 ^ []), implies(or(485 ^ [], 486 ^ []), or(485 ^ [], 487 ^ [])))), -(r5)], (493 ^ _109033) ^ [] : [op_or, 496 ^ _109033 : [(497 ^ _109033) ^ [_124197, _124199] : [-(or(_124199, _124197) = (not and(not _124199, not _124197)))]]], (499 ^ _109033) ^ [] : [op_and, 502 ^ _109033 : [(503 ^ _109033) ^ [_124370, _124372] : [-(and(_124372, _124370) = (not or(not _124372, not _124370)))]]], (505 ^ _109033) ^ [] : [op_implies_and, 508 ^ _109033 : [(509 ^ _109033) ^ [_124543, _124545] : [-(implies(_124545, _124543) = (not and(_124545, not _124543)))]]], (511 ^ _109033) ^ [] : [op_implies_or, 514 ^ _109033 : [(515 ^ _109033) ^ [_124714, _124716] : [-(implies(_124716, _124714) = or(not _124716, _124714))]]], (517 ^ _109033) ^ [] : [op_equiv, 520 ^ _109033 : [(521 ^ _109033) ^ [_124863, _124865] : [-(equiv(_124865, _124863) = and(implies(_124865, _124863), implies(_124863, _124865)))]]], (523 ^ _109033) ^ [] : [-(op_or)], (525 ^ _109033) ^ [] : [-(op_implies_and)], (527 ^ _109033) ^ [] : [-(op_equiv)], (529 ^ _109033) ^ [] : [-(modus_ponens)], (531 ^ _109033) ^ [] : [-(modus_tollens)], (533 ^ _109033) ^ [] : [-(implies_1)], (535 ^ _109033) ^ [] : [-(implies_2)], (537 ^ _109033) ^ [] : [-(implies_3)], (539 ^ _109033) ^ [] : [-(and_1)], (541 ^ _109033) ^ [] : [-(and_2)], (543 ^ _109033) ^ [] : [-(and_3)], (545 ^ _109033) ^ [] : [-(or_1)], (547 ^ _109033) ^ [] : [-(or_2)], (549 ^ _109033) ^ [] : [-(or_3)], (551 ^ _109033) ^ [] : [-(equivalence_1)], (553 ^ _109033) ^ [] : [-(equivalence_2)], (555 ^ _109033) ^ [] : [-(equivalence_3)], (557 ^ _109033) ^ [] : [-(substitution_of_equivalents)], (934 ^ _109033) ^ [] : [-(op_possibly)], (936 ^ _109033) ^ [] : [-(necessitation)], (938 ^ _109033) ^ [] : [-(axiom_K)], (940 ^ _109033) ^ [] : [-(axiom_M)], (942 ^ _109033) ^ [] : [-(axiom_4)], (944 ^ _109033) ^ [] : [-(axiom_B)], (946 ^ _109033) ^ [] : [-(op_possibly)], (948 ^ _109033) ^ [] : [-(op_or)], (950 ^ _109033) ^ [] : [-(op_implies)], (952 ^ _109033) ^ [] : [-(op_strict_implies)], (954 ^ _109033) ^ [] : [-(op_equiv)], (956 ^ _109033) ^ [] : [-(op_strict_equiv)], (910 ^ _109033) ^ [] : [op_possibly, 913 ^ _109033 : [(914 ^ _109033) ^ [_135868] : [-(possibly(_135868) = (not necessarily(not _135868)))]]], (916 ^ _109033) ^ [] : [op_necessarily, 919 ^ _109033 : [(920 ^ _109033) ^ [_136021] : [-(necessarily(_136021) = (not possibly(not _136021)))]]], (922 ^ _109033) ^ [] : [op_strict_implies, 925 ^ _109033 : [(926 ^ _109033) ^ [_136188, _136190] : [-(strict_implies(_136190, _136188) = necessarily(implies(_136190, _136188)))]]], (928 ^ _109033) ^ [] : [op_strict_equiv, 931 ^ _109033 : [(932 ^ _109033) ^ [_136337, _136339] : [-(strict_equiv(_136339, _136337) = and(strict_implies(_136339, _136337), strict_implies(_136337, _136339)))]]], (569 ^ _109033) ^ [] : [571 ^ _109033 : [(572 ^ _109033) ^ [] : [-(is_a_theorem(570 ^ []))], (574 ^ _109033) ^ [] : [is_a_theorem(necessarily(570 ^ []))]], -(necessitation)], (559 ^ _109033) ^ [] : [necessitation, 562 ^ _109033 : [(563 ^ _109033) ^ [_126082] : [is_a_theorem(_126082), -(is_a_theorem(necessarily(_126082)))]]], (592 ^ _109033) ^ [] : [595 ^ _109033 : [(596 ^ _109033) ^ [] : [-(is_a_theorem(593 ^ []))], (598 ^ _109033) ^ [] : [-(is_a_theorem(strict_implies(593 ^ [], 594 ^ [])))], (600 ^ _109033) ^ [] : [is_a_theorem(594 ^ [])]], -(modus_ponens_strict_implies)], (578 ^ _109033) ^ [] : [modus_ponens_strict_implies, 581 ^ _109033 : [(582 ^ _109033) ^ [_126582, _126584] : [-(is_a_theorem(_126582)), is_a_theorem(_126584), is_a_theorem(strict_implies(_126584, _126582))]]], (618 ^ _109033) ^ [] : [621 ^ _109033 : [(622 ^ _109033) ^ [] : [-(is_a_theorem(619 ^ []))], (624 ^ _109033) ^ [] : [-(is_a_theorem(620 ^ []))], (626 ^ _109033) ^ [] : [is_a_theorem(and(619 ^ [], 620 ^ []))]], -(adjunction)], (604 ^ _109033) ^ [] : [adjunction, 607 ^ _109033 : [(608 ^ _109033) ^ [_127292, _127294] : [-(is_a_theorem(and(_127294, _127292))), is_a_theorem(_127294), is_a_theorem(_127292)]]], (640 ^ _109033) ^ [] : [643 ^ _109033 : [(644 ^ _109033) ^ [] : [-(is_a_theorem(strict_equiv(641 ^ [], 642 ^ [])))], (646 ^ _109033) ^ [] : [641 ^ [] = 642 ^ []]], -(substitution_strict_equiv)], (630 ^ _109033) ^ [] : [substitution_strict_equiv, 633 ^ _109033 : [(634 ^ _109033) ^ [_128002, _128004] : [is_a_theorem(strict_equiv(_128004, _128002)), -(_128004 = _128002)]]], (650 ^ _109033) ^ [] : [axiom_K, 653 ^ _109033 : [(654 ^ _109033) ^ [_128549, _128551] : [-(is_a_theorem(implies(necessarily(implies(_128551, _128549)), implies(necessarily(_128551), necessarily(_128549)))))]]], (656 ^ _109033) ^ [] : [is_a_theorem(implies(necessarily(implies(657 ^ [], 658 ^ [])), implies(necessarily(657 ^ []), necessarily(658 ^ [])))), -(axiom_K)], (664 ^ _109033) ^ [] : [axiom_M, 667 ^ _109033 : [(668 ^ _109033) ^ [_128945] : [-(is_a_theorem(implies(necessarily(_128945), _128945)))]]], (670 ^ _109033) ^ [] : [is_a_theorem(implies(necessarily(671 ^ []), 671 ^ [])), -(axiom_M)], (677 ^ _109033) ^ [] : [axiom_4, 680 ^ _109033 : [(681 ^ _109033) ^ [_129265] : [-(is_a_theorem(implies(necessarily(_129265), necessarily(necessarily(_129265)))))]]], (683 ^ _109033) ^ [] : [is_a_theorem(implies(necessarily(684 ^ []), necessarily(necessarily(684 ^ [])))), -(axiom_4)], (690 ^ _109033) ^ [] : [axiom_B, 693 ^ _109033 : [(694 ^ _109033) ^ [_129593] : [-(is_a_theorem(implies(_129593, necessarily(possibly(_129593)))))]]], (696 ^ _109033) ^ [] : [is_a_theorem(implies(697 ^ [], necessarily(possibly(697 ^ [])))), -(axiom_B)], (703 ^ _109033) ^ [] : [axiom_5, 706 ^ _109033 : [(707 ^ _109033) ^ [_129917] : [-(is_a_theorem(implies(possibly(_129917), necessarily(possibly(_129917)))))]]], (709 ^ _109033) ^ [] : [is_a_theorem(implies(possibly(710 ^ []), necessarily(possibly(710 ^ [])))), -(axiom_5)], (716 ^ _109033) ^ [] : [axiom_s1, 719 ^ _109033 : [(720 ^ _109033) ^ [_130273, _130275, _130277] : [-(is_a_theorem(implies(and(necessarily(implies(_130277, _130275)), necessarily(implies(_130275, _130273))), necessarily(implies(_130277, _130273)))))]]], (722 ^ _109033) ^ [] : [is_a_theorem(implies(and(necessarily(implies(723 ^ [], 724 ^ [])), necessarily(implies(724 ^ [], 725 ^ []))), necessarily(implies(723 ^ [], 725 ^ [])))), -(axiom_s1)], (731 ^ _109033) ^ [] : [axiom_s2, 734 ^ _109033 : [(735 ^ _109033) ^ [_130767, _130769] : [-(is_a_theorem(strict_implies(possibly(and(_130769, _130767)), and(possibly(_130769), possibly(_130767)))))]]], (737 ^ _109033) ^ [] : [is_a_theorem(strict_implies(possibly(and(738 ^ [], 739 ^ [])), and(possibly(738 ^ []), possibly(739 ^ [])))), -(axiom_s2)], (745 ^ _109033) ^ [] : [axiom_s3, 748 ^ _109033 : [(749 ^ _109033) ^ [_131177, _131179] : [-(is_a_theorem(strict_implies(strict_implies(_131179, _131177), strict_implies(not possibly(_131177), not possibly(_131179)))))]]], (751 ^ _109033) ^ [] : [is_a_theorem(strict_implies(strict_implies(752 ^ [], 753 ^ []), strict_implies(not possibly(753 ^ []), not possibly(752 ^ [])))), -(axiom_s3)], (759 ^ _109033) ^ [] : [axiom_s4, 762 ^ _109033 : [(763 ^ _109033) ^ [_131577] : [-(is_a_theorem(strict_implies(necessarily(_131577), necessarily(necessarily(_131577)))))]]], (765 ^ _109033) ^ [] : [is_a_theorem(strict_implies(necessarily(766 ^ []), necessarily(necessarily(766 ^ [])))), -(axiom_s4)], (772 ^ _109033) ^ [] : [axiom_m1, 775 ^ _109033 : [(776 ^ _109033) ^ [_131919, _131921] : [-(is_a_theorem(strict_implies(and(_131921, _131919), and(_131919, _131921))))]]], (778 ^ _109033) ^ [] : [is_a_theorem(strict_implies(and(779 ^ [], 780 ^ []), and(780 ^ [], 779 ^ []))), -(axiom_m1)], (786 ^ _109033) ^ [] : [axiom_m2, 789 ^ _109033 : [(790 ^ _109033) ^ [_132313, _132315] : [-(is_a_theorem(strict_implies(and(_132315, _132313), _132315)))]]], (792 ^ _109033) ^ [] : [is_a_theorem(strict_implies(and(793 ^ [], 794 ^ []), 793 ^ [])), -(axiom_m2)], (800 ^ _109033) ^ [] : [axiom_m3, 803 ^ _109033 : [(804 ^ _109033) ^ [_132712, _132714, _132716] : [-(is_a_theorem(strict_implies(and(and(_132716, _132714), _132712), and(_132716, and(_132714, _132712)))))]]], (806 ^ _109033) ^ [] : [is_a_theorem(strict_implies(and(and(807 ^ [], 808 ^ []), 809 ^ []), and(807 ^ [], and(808 ^ [], 809 ^ [])))), -(axiom_m3)], (815 ^ _109033) ^ [] : [axiom_m4, 818 ^ _109033 : [(819 ^ _109033) ^ [_133170] : [-(is_a_theorem(strict_implies(_133170, and(_133170, _133170))))]]], (821 ^ _109033) ^ [] : [is_a_theorem(strict_implies(822 ^ [], and(822 ^ [], 822 ^ []))), -(axiom_m4)], (828 ^ _109033) ^ [] : [axiom_m5, 831 ^ _109033 : [(832 ^ _109033) ^ [_133520, _133522, _133524] : [-(is_a_theorem(strict_implies(and(strict_implies(_133524, _133522), strict_implies(_133522, _133520)), strict_implies(_133524, _133520))))]]], (834 ^ _109033) ^ [] : [is_a_theorem(strict_implies(and(strict_implies(835 ^ [], 836 ^ []), strict_implies(836 ^ [], 837 ^ [])), strict_implies(835 ^ [], 837 ^ []))), -(axiom_m5)], (843 ^ _109033) ^ [] : [axiom_m6, 846 ^ _109033 : [(847 ^ _109033) ^ [_133978] : [-(is_a_theorem(strict_implies(_133978, possibly(_133978))))]]], (849 ^ _109033) ^ [] : [is_a_theorem(strict_implies(850 ^ [], possibly(850 ^ []))), -(axiom_m6)], (856 ^ _109033) ^ [] : [axiom_m7, 859 ^ _109033 : [(860 ^ _109033) ^ [_134312, _134314] : [-(is_a_theorem(strict_implies(possibly(and(_134314, _134312)), _134314)))]]], (862 ^ _109033) ^ [] : [is_a_theorem(strict_implies(possibly(and(863 ^ [], 864 ^ [])), 863 ^ [])), -(axiom_m7)], (870 ^ _109033) ^ [] : [axiom_m8, 873 ^ _109033 : [(874 ^ _109033) ^ [_134703, _134705] : [-(is_a_theorem(strict_implies(strict_implies(_134705, _134703), strict_implies(possibly(_134705), possibly(_134703)))))]]], (876 ^ _109033) ^ [] : [is_a_theorem(strict_implies(strict_implies(877 ^ [], 878 ^ []), strict_implies(possibly(877 ^ []), possibly(878 ^ [])))), -(axiom_m8)], (884 ^ _109033) ^ [] : [axiom_m9, 887 ^ _109033 : [(888 ^ _109033) ^ [_135093] : [-(is_a_theorem(strict_implies(possibly(possibly(_135093)), possibly(_135093))))]]], (890 ^ _109033) ^ [] : [is_a_theorem(strict_implies(possibly(possibly(891 ^ [])), possibly(891 ^ []))), -(axiom_m9)], (897 ^ _109033) ^ [] : [axiom_m10, 900 ^ _109033 : [(901 ^ _109033) ^ [_135401] : [-(is_a_theorem(strict_implies(possibly(_135401), necessarily(possibly(_135401)))))]]], (903 ^ _109033) ^ [] : [is_a_theorem(strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))), -(axiom_m10)]], input).
% 18.25/17.97  ncf('1',plain,[axiom_m4],start(958 ^ 0)).
% 18.25/17.97  ncf('1.1',plain,[-(axiom_m4), is_a_theorem(strict_implies(822 ^ [], and(822 ^ [], 822 ^ [])))],extension(821 ^ 1)).
% 18.25/17.97  ncf('1.1.1',plain,[-(is_a_theorem(strict_implies(822 ^ [], and(822 ^ [], 822 ^ [])))), necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))) = strict_implies(822 ^ [], and(822 ^ [], 822 ^ [])), is_a_theorem(necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))))],extension(20 ^ 2,bind([[_109781, _109783], [strict_implies(822 ^ [], and(822 ^ [], 822 ^ [])), necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ [])))]]))).
% 18.25/17.97  ncf('1.1.1.1',plain,[-(necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))) = strict_implies(822 ^ [], and(822 ^ [], 822 ^ []))), strict_implies(822 ^ [], and(822 ^ [], 822 ^ [])) = necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ [])))],extension(4 ^ 3,bind([[_109284, _109286], [necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))), strict_implies(822 ^ [], and(822 ^ [], 822 ^ []))]]))).
% 18.25/17.97  ncf('1.1.1.1.1',plain,[-(strict_implies(822 ^ [], and(822 ^ [], 822 ^ [])) = necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ [])))), strict_implies(822 ^ [], and(822 ^ [], 822 ^ [])) = necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))), necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))) = necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ [])))],extension(10 ^ 4,bind([[_109488, _109490, _109492], [necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))), necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))), strict_implies(822 ^ [], and(822 ^ [], 822 ^ []))]]))).
% 18.25/17.97  ncf('1.1.1.1.1.1',plain,[-(strict_implies(822 ^ [], and(822 ^ [], 822 ^ [])) = necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ [])))), op_strict_implies],extension(922 ^ 5,bind([[_136188, _136190], [and(822 ^ [], 822 ^ []), 822 ^ []]]))).
% 18.25/17.97  ncf('1.1.1.1.1.1.1',plain,[-(op_strict_implies)],extension(952 ^ 6)).
% 18.25/17.97  ncf('1.1.1.1.1.2',plain,[-(necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))) = necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))))],extension(2 ^ 5,bind([[_109177], [necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ [])))]]))).
% 18.25/17.97  ncf('1.1.1.2',plain,[-(is_a_theorem(necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))))), 563 : is_a_theorem(implies(822 ^ [], and(822 ^ [], 822 ^ []))), 563 : necessitation],extension(559 ^ 3,bind([[_126082], [implies(822 ^ [], and(822 ^ [], 822 ^ []))]]))).
% 18.25/17.97  ncf('1.1.1.2.1',plain,[-(is_a_theorem(implies(822 ^ [], and(822 ^ [], 822 ^ [])))), 112 : is_a_theorem(implies(822 ^ [], implies(822 ^ [], and(822 ^ [], 822 ^ [])))), 112 : is_a_theorem(implies(implies(822 ^ [], implies(822 ^ [], and(822 ^ [], 822 ^ []))), implies(822 ^ [], and(822 ^ [], 822 ^ [])))), 112 : modus_ponens],extension(108 ^ 6,bind([[_113001, _113003], [implies(822 ^ [], and(822 ^ [], 822 ^ [])), implies(822 ^ [], implies(822 ^ [], and(822 ^ [], 822 ^ [])))]]))).
% 18.25/17.97  ncf('1.1.1.2.1.1',plain,[-(is_a_theorem(implies(822 ^ [], implies(822 ^ [], and(822 ^ [], 822 ^ []))))), and_3],extension(239 ^ 9,bind([[_116706, _116708], [822 ^ [], 822 ^ []]]))).
% 18.25/17.97  ncf('1.1.1.2.1.1.1',plain,[-(and_3)],extension(543 ^ 10)).
% 18.25/17.97  ncf('1.1.1.2.1.2',plain,[-(is_a_theorem(implies(implies(822 ^ [], implies(822 ^ [], and(822 ^ [], 822 ^ []))), implies(822 ^ [], and(822 ^ [], 822 ^ []))))), implies_2],extension(182 ^ 9,bind([[_115047, _115049], [and(822 ^ [], 822 ^ []), 822 ^ []]]))).
% 18.25/17.97  ncf('1.1.1.2.1.2.1',plain,[-(implies_2)],extension(535 ^ 10)).
% 18.25/17.97  ncf('1.1.1.2.1.3',plain,[-(modus_ponens)],extension(529 ^ 7)).
% 18.25/17.97  ncf('1.1.1.2.2',plain,[-(necessitation)],extension(936 ^ 4)).
% 18.25/17.97  %-----------------------------------------------------
% 18.25/17.97  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------