%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL542+1 : TPTP v8.1.2. Released v3.3.0.
% 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 11:33:27 EDT 2023

% Result   : Theorem 0.68s 1.38s
% Output   : Proof 0.68s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL542+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n027.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 16:03:05 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.68/1.38  
% 0.68/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.68/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.68/1.38  %-----------------------------------------------------
% 0.68/1.38  ncf(matrix, plain, [(958 ^ _107556) ^ [] : [axiom_m2], (20 ^ _107556) ^ [_108304, _108306] : [-(is_a_theorem(_108304)), _108306 = _108304, is_a_theorem(_108306)], (2 ^ _107556) ^ [_107700] : [-(_107700 = _107700)], (4 ^ _107556) ^ [_107807, _107809] : [_107809 = _107807, -(_107807 = _107809)], (10 ^ _107556) ^ [_108011, _108013, _108015] : [-(_108015 = _108011), _108015 = _108013, _108013 = _108011], (30 ^ _107556) ^ [_108629, _108631, _108633, _108635] : [-(or(_108635, _108631) = or(_108633, _108629)), _108635 = _108633, _108631 = _108629], (40 ^ _107556) ^ [_108988, _108990, _108992, _108994] : [-(equiv(_108994, _108990) = equiv(_108992, _108988)), _108994 = _108992, _108990 = _108988], (50 ^ _107556) ^ [_109319, _109321] : [_109321 = _109319, -(possibly(_109321) = possibly(_109319))], (56 ^ _107556) ^ [_109537, _109539] : [_109539 = _109537, -((not _109539) = (not _109537))], (62 ^ _107556) ^ [_109755, _109757] : [_109757 = _109755, -(necessarily(_109757) = necessarily(_109755))], (68 ^ _107556) ^ [_110001, _110003, _110005, _110007] : [-(implies(_110007, _110003) = implies(_110005, _110001)), _110007 = _110005, _110003 = _110001], (78 ^ _107556) ^ [_110360, _110362, _110364, _110366] : [-(strict_equiv(_110366, _110362) = strict_equiv(_110364, _110360)), _110366 = _110364, _110362 = _110360], (88 ^ _107556) ^ [_110719, _110721, _110723, _110725] : [-(and(_110725, _110721) = and(_110723, _110719)), _110725 = _110723, _110721 = _110719], (98 ^ _107556) ^ [_111058, _111060, _111062, _111064] : [-(strict_implies(_111064, _111060) = strict_implies(_111062, _111058)), _111064 = _111062, _111060 = _111058], (122 ^ _107556) ^ [] : [125 ^ _107556 : [(126 ^ _107556) ^ [] : [-(is_a_theorem(123 ^ []))], (128 ^ _107556) ^ [] : [-(is_a_theorem(implies(123 ^ [], 124 ^ [])))], (130 ^ _107556) ^ [] : [is_a_theorem(124 ^ [])]], -(modus_ponens)], (108 ^ _107556) ^ [] : [modus_ponens, 111 ^ _107556 : [(112 ^ _107556) ^ [_111524, _111526] : [-(is_a_theorem(_111524)), is_a_theorem(_111526), is_a_theorem(implies(_111526, _111524))]]], (144 ^ _107556) ^ [] : [147 ^ _107556 : [(148 ^ _107556) ^ [] : [-(is_a_theorem(equiv(145 ^ [], 146 ^ [])))], (150 ^ _107556) ^ [] : [145 ^ [] = 146 ^ []]], -(substitution_of_equivalents)], (134 ^ _107556) ^ [] : [substitution_of_equivalents, 137 ^ _107556 : [(138 ^ _107556) ^ [_112234, _112236] : [is_a_theorem(equiv(_112236, _112234)), -(_112236 = _112234)]]], (154 ^ _107556) ^ [] : [modus_tollens, 157 ^ _107556 : [(158 ^ _107556) ^ [_112781, _112783] : [-(is_a_theorem(implies(implies(not _112781, not _112783), implies(_112783, _112781))))]]], (160 ^ _107556) ^ [] : [is_a_theorem(implies(implies(not 162 ^ [], not 161 ^ []), implies(161 ^ [], 162 ^ []))), -(modus_tollens)], (168 ^ _107556) ^ [] : [implies_1, 171 ^ _107556 : [(172 ^ _107556) ^ [_113185, _113187] : [-(is_a_theorem(implies(_113187, implies(_113185, _113187))))]]], (174 ^ _107556) ^ [] : [is_a_theorem(implies(175 ^ [], implies(176 ^ [], 175 ^ []))), -(implies_1)], (182 ^ _107556) ^ [] : [implies_2, 185 ^ _107556 : [(186 ^ _107556) ^ [_113570, _113572] : [-(is_a_theorem(implies(implies(_113572, implies(_113572, _113570)), implies(_113572, _113570))))]]], (188 ^ _107556) ^ [] : [is_a_theorem(implies(implies(189 ^ [], implies(189 ^ [], 190 ^ [])), implies(189 ^ [], 190 ^ []))), -(implies_2)], (196 ^ _107556) ^ [] : [implies_3, 199 ^ _107556 : [(200 ^ _107556) ^ [_113987, _113989, _113991] : [-(is_a_theorem(implies(implies(_113991, _113989), implies(implies(_113989, _113987), implies(_113991, _113987)))))]]], (202 ^ _107556) ^ [] : [is_a_theorem(implies(implies(203 ^ [], 204 ^ []), implies(implies(204 ^ [], 205 ^ []), implies(203 ^ [], 205 ^ [])))), -(implies_3)], (211 ^ _107556) ^ [] : [and_1, 214 ^ _107556 : [(215 ^ _107556) ^ [_114459, _114461] : [-(is_a_theorem(implies(and(_114461, _114459), _114461)))]]], (217 ^ _107556) ^ [] : [is_a_theorem(implies(and(218 ^ [], 219 ^ []), 218 ^ [])), -(and_1)], (225 ^ _107556) ^ [] : [and_2, 228 ^ _107556 : [(229 ^ _107556) ^ [_114844, _114846] : [-(is_a_theorem(implies(and(_114846, _114844), _114844)))]]], (231 ^ _107556) ^ [] : [is_a_theorem(implies(and(232 ^ [], 233 ^ []), 233 ^ [])), -(and_2)], (239 ^ _107556) ^ [] : [and_3, 242 ^ _107556 : [(243 ^ _107556) ^ [_115229, _115231] : [-(is_a_theorem(implies(_115231, implies(_115229, and(_115231, _115229)))))]]], (245 ^ _107556) ^ [] : [is_a_theorem(implies(246 ^ [], implies(247 ^ [], and(246 ^ [], 247 ^ [])))), -(and_3)], (253 ^ _107556) ^ [] : [or_1, 256 ^ _107556 : [(257 ^ _107556) ^ [_115623, _115625] : [-(is_a_theorem(implies(_115625, or(_115625, _115623))))]]], (259 ^ _107556) ^ [] : [is_a_theorem(implies(260 ^ [], or(260 ^ [], 261 ^ []))), -(or_1)], (267 ^ _107556) ^ [] : [or_2, 270 ^ _107556 : [(271 ^ _107556) ^ [_116008, _116010] : [-(is_a_theorem(implies(_116008, or(_116010, _116008))))]]], (273 ^ _107556) ^ [] : [is_a_theorem(implies(275 ^ [], or(274 ^ [], 275 ^ []))), -(or_2)], (281 ^ _107556) ^ [] : [or_3, 284 ^ _107556 : [(285 ^ _107556) ^ [_116407, _116409, _116411] : [-(is_a_theorem(implies(implies(_116411, _116407), implies(implies(_116409, _116407), implies(or(_116411, _116409), _116407)))))]]], (287 ^ _107556) ^ [] : [is_a_theorem(implies(implies(288 ^ [], 290 ^ []), implies(implies(289 ^ [], 290 ^ []), implies(or(288 ^ [], 289 ^ []), 290 ^ [])))), -(or_3)], (296 ^ _107556) ^ [] : [equivalence_1, 299 ^ _107556 : [(300 ^ _107556) ^ [_116891, _116893] : [-(is_a_theorem(implies(equiv(_116893, _116891), implies(_116893, _116891))))]]], (302 ^ _107556) ^ [] : [is_a_theorem(implies(equiv(303 ^ [], 304 ^ []), implies(303 ^ [], 304 ^ []))), -(equivalence_1)], (310 ^ _107556) ^ [] : [equivalence_2, 313 ^ _107556 : [(314 ^ _107556) ^ [_117285, _117287] : [-(is_a_theorem(implies(equiv(_117287, _117285), implies(_117285, _117287))))]]], (316 ^ _107556) ^ [] : [is_a_theorem(implies(equiv(317 ^ [], 318 ^ []), implies(318 ^ [], 317 ^ []))), -(equivalence_2)], (324 ^ _107556) ^ [] : [equivalence_3, 327 ^ _107556 : [(328 ^ _107556) ^ [_117679, _117681] : [-(is_a_theorem(implies(implies(_117681, _117679), implies(implies(_117679, _117681), equiv(_117681, _117679)))))]]], (330 ^ _107556) ^ [] : [is_a_theorem(implies(implies(331 ^ [], 332 ^ []), implies(implies(332 ^ [], 331 ^ []), equiv(331 ^ [], 332 ^ [])))), -(equivalence_3)], (338 ^ _107556) ^ [] : [kn1, 341 ^ _107556 : [(342 ^ _107556) ^ [_118077] : [-(is_a_theorem(implies(_118077, and(_118077, _118077))))]]], (344 ^ _107556) ^ [] : [is_a_theorem(implies(345 ^ [], and(345 ^ [], 345 ^ []))), -(kn1)], (351 ^ _107556) ^ [] : [kn2, 354 ^ _107556 : [(355 ^ _107556) ^ [_118413, _118415] : [-(is_a_theorem(implies(and(_118415, _118413), _118415)))]]], (357 ^ _107556) ^ [] : [is_a_theorem(implies(and(358 ^ [], 359 ^ []), 358 ^ [])), -(kn2)], (365 ^ _107556) ^ [] : [kn3, 368 ^ _107556 : [(369 ^ _107556) ^ [_118812, _118814, _118816] : [-(is_a_theorem(implies(implies(_118816, _118814), implies(not and(_118814, _118812), not and(_118812, _118816)))))]]], (371 ^ _107556) ^ [] : [is_a_theorem(implies(implies(372 ^ [], 373 ^ []), implies(not and(373 ^ [], 374 ^ []), not and(374 ^ [], 372 ^ [])))), -(kn3)], (380 ^ _107556) ^ [] : [cn1, 383 ^ _107556 : [(384 ^ _107556) ^ [_119314, _119316, _119318] : [-(is_a_theorem(implies(implies(_119318, _119316), implies(implies(_119316, _119314), implies(_119318, _119314)))))]]], (386 ^ _107556) ^ [] : [is_a_theorem(implies(implies(387 ^ [], 388 ^ []), implies(implies(388 ^ [], 389 ^ []), implies(387 ^ [], 389 ^ [])))), -(cn1)], (395 ^ _107556) ^ [] : [cn2, 398 ^ _107556 : [(399 ^ _107556) ^ [_119786, _119788] : [-(is_a_theorem(implies(_119788, implies(not _119788, _119786))))]]], (401 ^ _107556) ^ [] : [is_a_theorem(implies(402 ^ [], implies(not 402 ^ [], 403 ^ []))), -(cn2)], (409 ^ _107556) ^ [] : [cn3, 412 ^ _107556 : [(413 ^ _107556) ^ [_120161] : [-(is_a_theorem(implies(implies(not _120161, _120161), _120161)))]]], (415 ^ _107556) ^ [] : [is_a_theorem(implies(implies(not 416 ^ [], 416 ^ []), 416 ^ [])), -(cn3)], (422 ^ _107556) ^ [] : [r1, 425 ^ _107556 : [(426 ^ _107556) ^ [_120487] : [-(is_a_theorem(implies(or(_120487, _120487), _120487)))]]], (428 ^ _107556) ^ [] : [is_a_theorem(implies(or(429 ^ [], 429 ^ []), 429 ^ [])), -(r1)], (435 ^ _107556) ^ [] : [r2, 438 ^ _107556 : [(439 ^ _107556) ^ [_120823, _120825] : [-(is_a_theorem(implies(_120823, or(_120825, _120823))))]]], (441 ^ _107556) ^ [] : [is_a_theorem(implies(443 ^ [], or(442 ^ [], 443 ^ []))), -(r2)], (449 ^ _107556) ^ [] : [r3, 452 ^ _107556 : [(453 ^ _107556) ^ [_121208, _121210] : [-(is_a_theorem(implies(or(_121210, _121208), or(_121208, _121210))))]]], (455 ^ _107556) ^ [] : [is_a_theorem(implies(or(456 ^ [], 457 ^ []), or(457 ^ [], 456 ^ []))), -(r3)], (463 ^ _107556) ^ [] : [r4, 466 ^ _107556 : [(467 ^ _107556) ^ [_121616, _121618, _121620] : [-(is_a_theorem(implies(or(_121620, or(_121618, _121616)), or(_121618, or(_121620, _121616)))))]]], (469 ^ _107556) ^ [] : [is_a_theorem(implies(or(470 ^ [], or(471 ^ [], 472 ^ [])), or(471 ^ [], or(470 ^ [], 472 ^ [])))), -(r4)], (478 ^ _107556) ^ [] : [r5, 481 ^ _107556 : [(482 ^ _107556) ^ [_122085, _122087, _122089] : [-(is_a_theorem(implies(implies(_122087, _122085), implies(or(_122089, _122087), or(_122089, _122085)))))]]], (484 ^ _107556) ^ [] : [is_a_theorem(implies(implies(486 ^ [], 487 ^ []), implies(or(485 ^ [], 486 ^ []), or(485 ^ [], 487 ^ [])))), -(r5)], (493 ^ _107556) ^ [] : [op_or, 496 ^ _107556 : [(497 ^ _107556) ^ [_122720, _122722] : [-(or(_122722, _122720) = (not and(not _122722, not _122720)))]]], (499 ^ _107556) ^ [] : [op_and, 502 ^ _107556 : [(503 ^ _107556) ^ [_122893, _122895] : [-(and(_122895, _122893) = (not or(not _122895, not _122893)))]]], (505 ^ _107556) ^ [] : [op_implies_and, 508 ^ _107556 : [(509 ^ _107556) ^ [_123066, _123068] : [-(implies(_123068, _123066) = (not and(_123068, not _123066)))]]], (511 ^ _107556) ^ [] : [op_implies_or, 514 ^ _107556 : [(515 ^ _107556) ^ [_123237, _123239] : [-(implies(_123239, _123237) = or(not _123239, _123237))]]], (517 ^ _107556) ^ [] : [op_equiv, 520 ^ _107556 : [(521 ^ _107556) ^ [_123386, _123388] : [-(equiv(_123388, _123386) = and(implies(_123388, _123386), implies(_123386, _123388)))]]], (523 ^ _107556) ^ [] : [-(op_or)], (525 ^ _107556) ^ [] : [-(op_implies_and)], (527 ^ _107556) ^ [] : [-(op_equiv)], (529 ^ _107556) ^ [] : [-(modus_ponens)], (531 ^ _107556) ^ [] : [-(modus_tollens)], (533 ^ _107556) ^ [] : [-(implies_1)], (535 ^ _107556) ^ [] : [-(implies_2)], (537 ^ _107556) ^ [] : [-(implies_3)], (539 ^ _107556) ^ [] : [-(and_1)], (541 ^ _107556) ^ [] : [-(and_2)], (543 ^ _107556) ^ [] : [-(and_3)], (545 ^ _107556) ^ [] : [-(or_1)], (547 ^ _107556) ^ [] : [-(or_2)], (549 ^ _107556) ^ [] : [-(or_3)], (551 ^ _107556) ^ [] : [-(equivalence_1)], (553 ^ _107556) ^ [] : [-(equivalence_2)], (555 ^ _107556) ^ [] : [-(equivalence_3)], (557 ^ _107556) ^ [] : [-(substitution_of_equivalents)], (934 ^ _107556) ^ [] : [-(op_possibly)], (936 ^ _107556) ^ [] : [-(necessitation)], (938 ^ _107556) ^ [] : [-(axiom_K)], (940 ^ _107556) ^ [] : [-(axiom_M)], (942 ^ _107556) ^ [] : [-(axiom_4)], (944 ^ _107556) ^ [] : [-(axiom_B)], (946 ^ _107556) ^ [] : [-(op_possibly)], (948 ^ _107556) ^ [] : [-(op_or)], (950 ^ _107556) ^ [] : [-(op_implies)], (952 ^ _107556) ^ [] : [-(op_strict_implies)], (954 ^ _107556) ^ [] : [-(op_equiv)], (956 ^ _107556) ^ [] : [-(op_strict_equiv)], (910 ^ _107556) ^ [] : [op_possibly, 913 ^ _107556 : [(914 ^ _107556) ^ [_134391] : [-(possibly(_134391) = (not necessarily(not _134391)))]]], (916 ^ _107556) ^ [] : [op_necessarily, 919 ^ _107556 : [(920 ^ _107556) ^ [_134544] : [-(necessarily(_134544) = (not possibly(not _134544)))]]], (922 ^ _107556) ^ [] : [op_strict_implies, 925 ^ _107556 : [(926 ^ _107556) ^ [_134711, _134713] : [-(strict_implies(_134713, _134711) = necessarily(implies(_134713, _134711)))]]], (928 ^ _107556) ^ [] : [op_strict_equiv, 931 ^ _107556 : [(932 ^ _107556) ^ [_134860, _134862] : [-(strict_equiv(_134862, _134860) = and(strict_implies(_134862, _134860), strict_implies(_134860, _134862)))]]], (569 ^ _107556) ^ [] : [571 ^ _107556 : [(572 ^ _107556) ^ [] : [-(is_a_theorem(570 ^ []))], (574 ^ _107556) ^ [] : [is_a_theorem(necessarily(570 ^ []))]], -(necessitation)], (559 ^ _107556) ^ [] : [necessitation, 562 ^ _107556 : [(563 ^ _107556) ^ [_124605] : [is_a_theorem(_124605), -(is_a_theorem(necessarily(_124605)))]]], (592 ^ _107556) ^ [] : [595 ^ _107556 : [(596 ^ _107556) ^ [] : [-(is_a_theorem(593 ^ []))], (598 ^ _107556) ^ [] : [-(is_a_theorem(strict_implies(593 ^ [], 594 ^ [])))], (600 ^ _107556) ^ [] : [is_a_theorem(594 ^ [])]], -(modus_ponens_strict_implies)], (578 ^ _107556) ^ [] : [modus_ponens_strict_implies, 581 ^ _107556 : [(582 ^ _107556) ^ [_125105, _125107] : [-(is_a_theorem(_125105)), is_a_theorem(_125107), is_a_theorem(strict_implies(_125107, _125105))]]], (618 ^ _107556) ^ [] : [621 ^ _107556 : [(622 ^ _107556) ^ [] : [-(is_a_theorem(619 ^ []))], (624 ^ _107556) ^ [] : [-(is_a_theorem(620 ^ []))], (626 ^ _107556) ^ [] : [is_a_theorem(and(619 ^ [], 620 ^ []))]], -(adjunction)], (604 ^ _107556) ^ [] : [adjunction, 607 ^ _107556 : [(608 ^ _107556) ^ [_125815, _125817] : [-(is_a_theorem(and(_125817, _125815))), is_a_theorem(_125817), is_a_theorem(_125815)]]], (640 ^ _107556) ^ [] : [643 ^ _107556 : [(644 ^ _107556) ^ [] : [-(is_a_theorem(strict_equiv(641 ^ [], 642 ^ [])))], (646 ^ _107556) ^ [] : [641 ^ [] = 642 ^ []]], -(substitution_strict_equiv)], (630 ^ _107556) ^ [] : [substitution_strict_equiv, 633 ^ _107556 : [(634 ^ _107556) ^ [_126525, _126527] : [is_a_theorem(strict_equiv(_126527, _126525)), -(_126527 = _126525)]]], (650 ^ _107556) ^ [] : [axiom_K, 653 ^ _107556 : [(654 ^ _107556) ^ [_127072, _127074] : [-(is_a_theorem(implies(necessarily(implies(_127074, _127072)), implies(necessarily(_127074), necessarily(_127072)))))]]], (656 ^ _107556) ^ [] : [is_a_theorem(implies(necessarily(implies(657 ^ [], 658 ^ [])), implies(necessarily(657 ^ []), necessarily(658 ^ [])))), -(axiom_K)], (664 ^ _107556) ^ [] : [axiom_M, 667 ^ _107556 : [(668 ^ _107556) ^ [_127468] : [-(is_a_theorem(implies(necessarily(_127468), _127468)))]]], (670 ^ _107556) ^ [] : [is_a_theorem(implies(necessarily(671 ^ []), 671 ^ [])), -(axiom_M)], (677 ^ _107556) ^ [] : [axiom_4, 680 ^ _107556 : [(681 ^ _107556) ^ [_127788] : [-(is_a_theorem(implies(necessarily(_127788), necessarily(necessarily(_127788)))))]]], (683 ^ _107556) ^ [] : [is_a_theorem(implies(necessarily(684 ^ []), necessarily(necessarily(684 ^ [])))), -(axiom_4)], (690 ^ _107556) ^ [] : [axiom_B, 693 ^ _107556 : [(694 ^ _107556) ^ [_128116] : [-(is_a_theorem(implies(_128116, necessarily(possibly(_128116)))))]]], (696 ^ _107556) ^ [] : [is_a_theorem(implies(697 ^ [], necessarily(possibly(697 ^ [])))), -(axiom_B)], (703 ^ _107556) ^ [] : [axiom_5, 706 ^ _107556 : [(707 ^ _107556) ^ [_128440] : [-(is_a_theorem(implies(possibly(_128440), necessarily(possibly(_128440)))))]]], (709 ^ _107556) ^ [] : [is_a_theorem(implies(possibly(710 ^ []), necessarily(possibly(710 ^ [])))), -(axiom_5)], (716 ^ _107556) ^ [] : [axiom_s1, 719 ^ _107556 : [(720 ^ _107556) ^ [_128796, _128798, _128800] : [-(is_a_theorem(implies(and(necessarily(implies(_128800, _128798)), necessarily(implies(_128798, _128796))), necessarily(implies(_128800, _128796)))))]]], (722 ^ _107556) ^ [] : [is_a_theorem(implies(and(necessarily(implies(723 ^ [], 724 ^ [])), necessarily(implies(724 ^ [], 725 ^ []))), necessarily(implies(723 ^ [], 725 ^ [])))), -(axiom_s1)], (731 ^ _107556) ^ [] : [axiom_s2, 734 ^ _107556 : [(735 ^ _107556) ^ [_129290, _129292] : [-(is_a_theorem(strict_implies(possibly(and(_129292, _129290)), and(possibly(_129292), possibly(_129290)))))]]], (737 ^ _107556) ^ [] : [is_a_theorem(strict_implies(possibly(and(738 ^ [], 739 ^ [])), and(possibly(738 ^ []), possibly(739 ^ [])))), -(axiom_s2)], (745 ^ _107556) ^ [] : [axiom_s3, 748 ^ _107556 : [(749 ^ _107556) ^ [_129700, _129702] : [-(is_a_theorem(strict_implies(strict_implies(_129702, _129700), strict_implies(not possibly(_129700), not possibly(_129702)))))]]], (751 ^ _107556) ^ [] : [is_a_theorem(strict_implies(strict_implies(752 ^ [], 753 ^ []), strict_implies(not possibly(753 ^ []), not possibly(752 ^ [])))), -(axiom_s3)], (759 ^ _107556) ^ [] : [axiom_s4, 762 ^ _107556 : [(763 ^ _107556) ^ [_130100] : [-(is_a_theorem(strict_implies(necessarily(_130100), necessarily(necessarily(_130100)))))]]], (765 ^ _107556) ^ [] : [is_a_theorem(strict_implies(necessarily(766 ^ []), necessarily(necessarily(766 ^ [])))), -(axiom_s4)], (772 ^ _107556) ^ [] : [axiom_m1, 775 ^ _107556 : [(776 ^ _107556) ^ [_130442, _130444] : [-(is_a_theorem(strict_implies(and(_130444, _130442), and(_130442, _130444))))]]], (778 ^ _107556) ^ [] : [is_a_theorem(strict_implies(and(779 ^ [], 780 ^ []), and(780 ^ [], 779 ^ []))), -(axiom_m1)], (786 ^ _107556) ^ [] : [axiom_m2, 789 ^ _107556 : [(790 ^ _107556) ^ [_130836, _130838] : [-(is_a_theorem(strict_implies(and(_130838, _130836), _130838)))]]], (792 ^ _107556) ^ [] : [is_a_theorem(strict_implies(and(793 ^ [], 794 ^ []), 793 ^ [])), -(axiom_m2)], (800 ^ _107556) ^ [] : [axiom_m3, 803 ^ _107556 : [(804 ^ _107556) ^ [_131235, _131237, _131239] : [-(is_a_theorem(strict_implies(and(and(_131239, _131237), _131235), and(_131239, and(_131237, _131235)))))]]], (806 ^ _107556) ^ [] : [is_a_theorem(strict_implies(and(and(807 ^ [], 808 ^ []), 809 ^ []), and(807 ^ [], and(808 ^ [], 809 ^ [])))), -(axiom_m3)], (815 ^ _107556) ^ [] : [axiom_m4, 818 ^ _107556 : [(819 ^ _107556) ^ [_131693] : [-(is_a_theorem(strict_implies(_131693, and(_131693, _131693))))]]], (821 ^ _107556) ^ [] : [is_a_theorem(strict_implies(822 ^ [], and(822 ^ [], 822 ^ []))), -(axiom_m4)], (828 ^ _107556) ^ [] : [axiom_m5, 831 ^ _107556 : [(832 ^ _107556) ^ [_132043, _132045, _132047] : [-(is_a_theorem(strict_implies(and(strict_implies(_132047, _132045), strict_implies(_132045, _132043)), strict_implies(_132047, _132043))))]]], (834 ^ _107556) ^ [] : [is_a_theorem(strict_implies(and(strict_implies(835 ^ [], 836 ^ []), strict_implies(836 ^ [], 837 ^ [])), strict_implies(835 ^ [], 837 ^ []))), -(axiom_m5)], (843 ^ _107556) ^ [] : [axiom_m6, 846 ^ _107556 : [(847 ^ _107556) ^ [_132501] : [-(is_a_theorem(strict_implies(_132501, possibly(_132501))))]]], (849 ^ _107556) ^ [] : [is_a_theorem(strict_implies(850 ^ [], possibly(850 ^ []))), -(axiom_m6)], (856 ^ _107556) ^ [] : [axiom_m7, 859 ^ _107556 : [(860 ^ _107556) ^ [_132835, _132837] : [-(is_a_theorem(strict_implies(possibly(and(_132837, _132835)), _132837)))]]], (862 ^ _107556) ^ [] : [is_a_theorem(strict_implies(possibly(and(863 ^ [], 864 ^ [])), 863 ^ [])), -(axiom_m7)], (870 ^ _107556) ^ [] : [axiom_m8, 873 ^ _107556 : [(874 ^ _107556) ^ [_133226, _133228] : [-(is_a_theorem(strict_implies(strict_implies(_133228, _133226), strict_implies(possibly(_133228), possibly(_133226)))))]]], (876 ^ _107556) ^ [] : [is_a_theorem(strict_implies(strict_implies(877 ^ [], 878 ^ []), strict_implies(possibly(877 ^ []), possibly(878 ^ [])))), -(axiom_m8)], (884 ^ _107556) ^ [] : [axiom_m9, 887 ^ _107556 : [(888 ^ _107556) ^ [_133616] : [-(is_a_theorem(strict_implies(possibly(possibly(_133616)), possibly(_133616))))]]], (890 ^ _107556) ^ [] : [is_a_theorem(strict_implies(possibly(possibly(891 ^ [])), possibly(891 ^ []))), -(axiom_m9)], (897 ^ _107556) ^ [] : [axiom_m10, 900 ^ _107556 : [(901 ^ _107556) ^ [_133924] : [-(is_a_theorem(strict_implies(possibly(_133924), necessarily(possibly(_133924)))))]]], (903 ^ _107556) ^ [] : [is_a_theorem(strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))), -(axiom_m10)]], input).
% 0.68/1.38  ncf('1',plain,[axiom_m2],start(958 ^ 0)).
% 0.68/1.38  ncf('1.1',plain,[-(axiom_m2), is_a_theorem(strict_implies(and(793 ^ [], 794 ^ []), 793 ^ []))],extension(792 ^ 1)).
% 0.68/1.38  ncf('1.1.1',plain,[-(is_a_theorem(strict_implies(and(793 ^ [], 794 ^ []), 793 ^ []))), necessarily(implies(and(793 ^ [], 794 ^ []), 793 ^ [])) = strict_implies(and(793 ^ [], 794 ^ []), 793 ^ []), is_a_theorem(necessarily(implies(and(793 ^ [], 794 ^ []), 793 ^ [])))],extension(20 ^ 2,bind([[_108304, _108306], [strict_implies(and(793 ^ [], 794 ^ []), 793 ^ []), necessarily(implies(and(793 ^ [], 794 ^ []), 793 ^ []))]]))).
% 0.68/1.38  ncf('1.1.1.1',plain,[-(necessarily(implies(and(793 ^ [], 794 ^ []), 793 ^ [])) = strict_implies(and(793 ^ [], 794 ^ []), 793 ^ [])), strict_implies(and(793 ^ [], 794 ^ []), 793 ^ []) = necessarily(implies(and(793 ^ [], 794 ^ []), 793 ^ []))],extension(4 ^ 3,bind([[_107807, _107809], [necessarily(implies(and(793 ^ [], 794 ^ []), 793 ^ [])), strict_implies(and(793 ^ [], 794 ^ []), 793 ^ [])]]))).
% 0.68/1.38  ncf('1.1.1.1.1',plain,[-(strict_implies(and(793 ^ [], 794 ^ []), 793 ^ []) = necessarily(implies(and(793 ^ [], 794 ^ []), 793 ^ []))), op_strict_implies],extension(922 ^ 4,bind([[_134711, _134713], [793 ^ [], and(793 ^ [], 794 ^ [])]]))).
% 0.68/1.38  ncf('1.1.1.1.1.1',plain,[-(op_strict_implies)],extension(952 ^ 5)).
% 0.68/1.38  ncf('1.1.1.2',plain,[-(is_a_theorem(necessarily(implies(and(793 ^ [], 794 ^ []), 793 ^ [])))), 563 : is_a_theorem(implies(and(793 ^ [], 794 ^ []), 793 ^ [])), 563 : necessitation],extension(559 ^ 3,bind([[_124605], [implies(and(793 ^ [], 794 ^ []), 793 ^ [])]]))).
% 0.68/1.38  ncf('1.1.1.2.1',plain,[-(is_a_theorem(implies(and(793 ^ [], 794 ^ []), 793 ^ []))), and_1],extension(211 ^ 6,bind([[_114459, _114461], [794 ^ [], 793 ^ []]]))).
% 0.68/1.38  ncf('1.1.1.2.1.1',plain,[-(and_1)],extension(539 ^ 7)).
% 0.68/1.38  ncf('1.1.1.2.2',plain,[-(necessitation)],extension(936 ^ 4)).
% 0.68/1.38  %-----------------------------------------------------
% 0.68/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------