%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL531+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n009.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 11:33:26 EDT 2023

% Result   : Theorem 15.00s 14.82s
% Output   : Proof 15.00s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL531+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n009.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 16:01:02 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 15.00/14.82  
% 15.00/14.82  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 15.00/14.82  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.00/14.82  %-----------------------------------------------------
% 15.00/14.82  ncf(matrix, plain, [(956 ^ _108838) ^ [] : [axiom_m4], (20 ^ _108838) ^ [_109586, _109588] : [-(is_a_theorem(_109586)), _109588 = _109586, is_a_theorem(_109588)], (2 ^ _108838) ^ [_108982] : [-(_108982 = _108982)], (4 ^ _108838) ^ [_109089, _109091] : [_109091 = _109089, -(_109089 = _109091)], (10 ^ _108838) ^ [_109293, _109295, _109297] : [-(_109297 = _109293), _109297 = _109295, _109295 = _109293], (30 ^ _108838) ^ [_109911, _109913, _109915, _109917] : [-(or(_109917, _109913) = or(_109915, _109911)), _109917 = _109915, _109913 = _109911], (40 ^ _108838) ^ [_110270, _110272, _110274, _110276] : [-(equiv(_110276, _110272) = equiv(_110274, _110270)), _110276 = _110274, _110272 = _110270], (50 ^ _108838) ^ [_110601, _110603] : [_110603 = _110601, -(possibly(_110603) = possibly(_110601))], (56 ^ _108838) ^ [_110819, _110821] : [_110821 = _110819, -((not _110821) = (not _110819))], (62 ^ _108838) ^ [_111037, _111039] : [_111039 = _111037, -(necessarily(_111039) = necessarily(_111037))], (68 ^ _108838) ^ [_111283, _111285, _111287, _111289] : [-(implies(_111289, _111285) = implies(_111287, _111283)), _111289 = _111287, _111285 = _111283], (78 ^ _108838) ^ [_111642, _111644, _111646, _111648] : [-(strict_equiv(_111648, _111644) = strict_equiv(_111646, _111642)), _111648 = _111646, _111644 = _111642], (88 ^ _108838) ^ [_112001, _112003, _112005, _112007] : [-(and(_112007, _112003) = and(_112005, _112001)), _112007 = _112005, _112003 = _112001], (98 ^ _108838) ^ [_112340, _112342, _112344, _112346] : [-(strict_implies(_112346, _112342) = strict_implies(_112344, _112340)), _112346 = _112344, _112342 = _112340], (122 ^ _108838) ^ [] : [125 ^ _108838 : [(126 ^ _108838) ^ [] : [-(is_a_theorem(123 ^ []))], (128 ^ _108838) ^ [] : [-(is_a_theorem(implies(123 ^ [], 124 ^ [])))], (130 ^ _108838) ^ [] : [is_a_theorem(124 ^ [])]], -(modus_ponens)], (108 ^ _108838) ^ [] : [modus_ponens, 111 ^ _108838 : [(112 ^ _108838) ^ [_112806, _112808] : [-(is_a_theorem(_112806)), is_a_theorem(_112808), is_a_theorem(implies(_112808, _112806))]]], (144 ^ _108838) ^ [] : [147 ^ _108838 : [(148 ^ _108838) ^ [] : [-(is_a_theorem(equiv(145 ^ [], 146 ^ [])))], (150 ^ _108838) ^ [] : [145 ^ [] = 146 ^ []]], -(substitution_of_equivalents)], (134 ^ _108838) ^ [] : [substitution_of_equivalents, 137 ^ _108838 : [(138 ^ _108838) ^ [_113516, _113518] : [is_a_theorem(equiv(_113518, _113516)), -(_113518 = _113516)]]], (154 ^ _108838) ^ [] : [modus_tollens, 157 ^ _108838 : [(158 ^ _108838) ^ [_114063, _114065] : [-(is_a_theorem(implies(implies(not _114063, not _114065), implies(_114065, _114063))))]]], (160 ^ _108838) ^ [] : [is_a_theorem(implies(implies(not 162 ^ [], not 161 ^ []), implies(161 ^ [], 162 ^ []))), -(modus_tollens)], (168 ^ _108838) ^ [] : [implies_1, 171 ^ _108838 : [(172 ^ _108838) ^ [_114467, _114469] : [-(is_a_theorem(implies(_114469, implies(_114467, _114469))))]]], (174 ^ _108838) ^ [] : [is_a_theorem(implies(175 ^ [], implies(176 ^ [], 175 ^ []))), -(implies_1)], (182 ^ _108838) ^ [] : [implies_2, 185 ^ _108838 : [(186 ^ _108838) ^ [_114852, _114854] : [-(is_a_theorem(implies(implies(_114854, implies(_114854, _114852)), implies(_114854, _114852))))]]], (188 ^ _108838) ^ [] : [is_a_theorem(implies(implies(189 ^ [], implies(189 ^ [], 190 ^ [])), implies(189 ^ [], 190 ^ []))), -(implies_2)], (196 ^ _108838) ^ [] : [implies_3, 199 ^ _108838 : [(200 ^ _108838) ^ [_115269, _115271, _115273] : [-(is_a_theorem(implies(implies(_115273, _115271), implies(implies(_115271, _115269), implies(_115273, _115269)))))]]], (202 ^ _108838) ^ [] : [is_a_theorem(implies(implies(203 ^ [], 204 ^ []), implies(implies(204 ^ [], 205 ^ []), implies(203 ^ [], 205 ^ [])))), -(implies_3)], (211 ^ _108838) ^ [] : [and_1, 214 ^ _108838 : [(215 ^ _108838) ^ [_115741, _115743] : [-(is_a_theorem(implies(and(_115743, _115741), _115743)))]]], (217 ^ _108838) ^ [] : [is_a_theorem(implies(and(218 ^ [], 219 ^ []), 218 ^ [])), -(and_1)], (225 ^ _108838) ^ [] : [and_2, 228 ^ _108838 : [(229 ^ _108838) ^ [_116126, _116128] : [-(is_a_theorem(implies(and(_116128, _116126), _116126)))]]], (231 ^ _108838) ^ [] : [is_a_theorem(implies(and(232 ^ [], 233 ^ []), 233 ^ [])), -(and_2)], (239 ^ _108838) ^ [] : [and_3, 242 ^ _108838 : [(243 ^ _108838) ^ [_116511, _116513] : [-(is_a_theorem(implies(_116513, implies(_116511, and(_116513, _116511)))))]]], (245 ^ _108838) ^ [] : [is_a_theorem(implies(246 ^ [], implies(247 ^ [], and(246 ^ [], 247 ^ [])))), -(and_3)], (253 ^ _108838) ^ [] : [or_1, 256 ^ _108838 : [(257 ^ _108838) ^ [_116905, _116907] : [-(is_a_theorem(implies(_116907, or(_116907, _116905))))]]], (259 ^ _108838) ^ [] : [is_a_theorem(implies(260 ^ [], or(260 ^ [], 261 ^ []))), -(or_1)], (267 ^ _108838) ^ [] : [or_2, 270 ^ _108838 : [(271 ^ _108838) ^ [_117290, _117292] : [-(is_a_theorem(implies(_117290, or(_117292, _117290))))]]], (273 ^ _108838) ^ [] : [is_a_theorem(implies(275 ^ [], or(274 ^ [], 275 ^ []))), -(or_2)], (281 ^ _108838) ^ [] : [or_3, 284 ^ _108838 : [(285 ^ _108838) ^ [_117689, _117691, _117693] : [-(is_a_theorem(implies(implies(_117693, _117689), implies(implies(_117691, _117689), implies(or(_117693, _117691), _117689)))))]]], (287 ^ _108838) ^ [] : [is_a_theorem(implies(implies(288 ^ [], 290 ^ []), implies(implies(289 ^ [], 290 ^ []), implies(or(288 ^ [], 289 ^ []), 290 ^ [])))), -(or_3)], (296 ^ _108838) ^ [] : [equivalence_1, 299 ^ _108838 : [(300 ^ _108838) ^ [_118173, _118175] : [-(is_a_theorem(implies(equiv(_118175, _118173), implies(_118175, _118173))))]]], (302 ^ _108838) ^ [] : [is_a_theorem(implies(equiv(303 ^ [], 304 ^ []), implies(303 ^ [], 304 ^ []))), -(equivalence_1)], (310 ^ _108838) ^ [] : [equivalence_2, 313 ^ _108838 : [(314 ^ _108838) ^ [_118567, _118569] : [-(is_a_theorem(implies(equiv(_118569, _118567), implies(_118567, _118569))))]]], (316 ^ _108838) ^ [] : [is_a_theorem(implies(equiv(317 ^ [], 318 ^ []), implies(318 ^ [], 317 ^ []))), -(equivalence_2)], (324 ^ _108838) ^ [] : [equivalence_3, 327 ^ _108838 : [(328 ^ _108838) ^ [_118961, _118963] : [-(is_a_theorem(implies(implies(_118963, _118961), implies(implies(_118961, _118963), equiv(_118963, _118961)))))]]], (330 ^ _108838) ^ [] : [is_a_theorem(implies(implies(331 ^ [], 332 ^ []), implies(implies(332 ^ [], 331 ^ []), equiv(331 ^ [], 332 ^ [])))), -(equivalence_3)], (338 ^ _108838) ^ [] : [kn1, 341 ^ _108838 : [(342 ^ _108838) ^ [_119359] : [-(is_a_theorem(implies(_119359, and(_119359, _119359))))]]], (344 ^ _108838) ^ [] : [is_a_theorem(implies(345 ^ [], and(345 ^ [], 345 ^ []))), -(kn1)], (351 ^ _108838) ^ [] : [kn2, 354 ^ _108838 : [(355 ^ _108838) ^ [_119695, _119697] : [-(is_a_theorem(implies(and(_119697, _119695), _119697)))]]], (357 ^ _108838) ^ [] : [is_a_theorem(implies(and(358 ^ [], 359 ^ []), 358 ^ [])), -(kn2)], (365 ^ _108838) ^ [] : [kn3, 368 ^ _108838 : [(369 ^ _108838) ^ [_120094, _120096, _120098] : [-(is_a_theorem(implies(implies(_120098, _120096), implies(not and(_120096, _120094), not and(_120094, _120098)))))]]], (371 ^ _108838) ^ [] : [is_a_theorem(implies(implies(372 ^ [], 373 ^ []), implies(not and(373 ^ [], 374 ^ []), not and(374 ^ [], 372 ^ [])))), -(kn3)], (380 ^ _108838) ^ [] : [cn1, 383 ^ _108838 : [(384 ^ _108838) ^ [_120596, _120598, _120600] : [-(is_a_theorem(implies(implies(_120600, _120598), implies(implies(_120598, _120596), implies(_120600, _120596)))))]]], (386 ^ _108838) ^ [] : [is_a_theorem(implies(implies(387 ^ [], 388 ^ []), implies(implies(388 ^ [], 389 ^ []), implies(387 ^ [], 389 ^ [])))), -(cn1)], (395 ^ _108838) ^ [] : [cn2, 398 ^ _108838 : [(399 ^ _108838) ^ [_121068, _121070] : [-(is_a_theorem(implies(_121070, implies(not _121070, _121068))))]]], (401 ^ _108838) ^ [] : [is_a_theorem(implies(402 ^ [], implies(not 402 ^ [], 403 ^ []))), -(cn2)], (409 ^ _108838) ^ [] : [cn3, 412 ^ _108838 : [(413 ^ _108838) ^ [_121443] : [-(is_a_theorem(implies(implies(not _121443, _121443), _121443)))]]], (415 ^ _108838) ^ [] : [is_a_theorem(implies(implies(not 416 ^ [], 416 ^ []), 416 ^ [])), -(cn3)], (422 ^ _108838) ^ [] : [r1, 425 ^ _108838 : [(426 ^ _108838) ^ [_121769] : [-(is_a_theorem(implies(or(_121769, _121769), _121769)))]]], (428 ^ _108838) ^ [] : [is_a_theorem(implies(or(429 ^ [], 429 ^ []), 429 ^ [])), -(r1)], (435 ^ _108838) ^ [] : [r2, 438 ^ _108838 : [(439 ^ _108838) ^ [_122105, _122107] : [-(is_a_theorem(implies(_122105, or(_122107, _122105))))]]], (441 ^ _108838) ^ [] : [is_a_theorem(implies(443 ^ [], or(442 ^ [], 443 ^ []))), -(r2)], (449 ^ _108838) ^ [] : [r3, 452 ^ _108838 : [(453 ^ _108838) ^ [_122490, _122492] : [-(is_a_theorem(implies(or(_122492, _122490), or(_122490, _122492))))]]], (455 ^ _108838) ^ [] : [is_a_theorem(implies(or(456 ^ [], 457 ^ []), or(457 ^ [], 456 ^ []))), -(r3)], (463 ^ _108838) ^ [] : [r4, 466 ^ _108838 : [(467 ^ _108838) ^ [_122898, _122900, _122902] : [-(is_a_theorem(implies(or(_122902, or(_122900, _122898)), or(_122900, or(_122902, _122898)))))]]], (469 ^ _108838) ^ [] : [is_a_theorem(implies(or(470 ^ [], or(471 ^ [], 472 ^ [])), or(471 ^ [], or(470 ^ [], 472 ^ [])))), -(r4)], (478 ^ _108838) ^ [] : [r5, 481 ^ _108838 : [(482 ^ _108838) ^ [_123367, _123369, _123371] : [-(is_a_theorem(implies(implies(_123369, _123367), implies(or(_123371, _123369), or(_123371, _123367)))))]]], (484 ^ _108838) ^ [] : [is_a_theorem(implies(implies(486 ^ [], 487 ^ []), implies(or(485 ^ [], 486 ^ []), or(485 ^ [], 487 ^ [])))), -(r5)], (493 ^ _108838) ^ [] : [op_or, 496 ^ _108838 : [(497 ^ _108838) ^ [_124002, _124004] : [-(or(_124004, _124002) = (not and(not _124004, not _124002)))]]], (499 ^ _108838) ^ [] : [op_and, 502 ^ _108838 : [(503 ^ _108838) ^ [_124175, _124177] : [-(and(_124177, _124175) = (not or(not _124177, not _124175)))]]], (505 ^ _108838) ^ [] : [op_implies_and, 508 ^ _108838 : [(509 ^ _108838) ^ [_124348, _124350] : [-(implies(_124350, _124348) = (not and(_124350, not _124348)))]]], (511 ^ _108838) ^ [] : [op_implies_or, 514 ^ _108838 : [(515 ^ _108838) ^ [_124519, _124521] : [-(implies(_124521, _124519) = or(not _124521, _124519))]]], (517 ^ _108838) ^ [] : [op_equiv, 520 ^ _108838 : [(521 ^ _108838) ^ [_124668, _124670] : [-(equiv(_124670, _124668) = and(implies(_124670, _124668), implies(_124668, _124670)))]]], (523 ^ _108838) ^ [] : [-(op_or)], (525 ^ _108838) ^ [] : [-(op_implies_and)], (527 ^ _108838) ^ [] : [-(op_equiv)], (529 ^ _108838) ^ [] : [-(modus_ponens)], (531 ^ _108838) ^ [] : [-(modus_tollens)], (533 ^ _108838) ^ [] : [-(implies_1)], (535 ^ _108838) ^ [] : [-(implies_2)], (537 ^ _108838) ^ [] : [-(implies_3)], (539 ^ _108838) ^ [] : [-(and_1)], (541 ^ _108838) ^ [] : [-(and_2)], (543 ^ _108838) ^ [] : [-(and_3)], (545 ^ _108838) ^ [] : [-(or_1)], (547 ^ _108838) ^ [] : [-(or_2)], (549 ^ _108838) ^ [] : [-(or_3)], (551 ^ _108838) ^ [] : [-(equivalence_1)], (553 ^ _108838) ^ [] : [-(equivalence_2)], (555 ^ _108838) ^ [] : [-(equivalence_3)], (557 ^ _108838) ^ [] : [-(substitution_of_equivalents)], (934 ^ _108838) ^ [] : [-(op_possibly)], (936 ^ _108838) ^ [] : [-(necessitation)], (938 ^ _108838) ^ [] : [-(axiom_K)], (940 ^ _108838) ^ [] : [-(axiom_M)], (942 ^ _108838) ^ [] : [-(axiom_5)], (944 ^ _108838) ^ [] : [-(op_possibly)], (946 ^ _108838) ^ [] : [-(op_or)], (948 ^ _108838) ^ [] : [-(op_implies)], (950 ^ _108838) ^ [] : [-(op_strict_implies)], (952 ^ _108838) ^ [] : [-(op_equiv)], (954 ^ _108838) ^ [] : [-(op_strict_equiv)], (910 ^ _108838) ^ [] : [op_possibly, 913 ^ _108838 : [(914 ^ _108838) ^ [_135673] : [-(possibly(_135673) = (not necessarily(not _135673)))]]], (916 ^ _108838) ^ [] : [op_necessarily, 919 ^ _108838 : [(920 ^ _108838) ^ [_135826] : [-(necessarily(_135826) = (not possibly(not _135826)))]]], (922 ^ _108838) ^ [] : [op_strict_implies, 925 ^ _108838 : [(926 ^ _108838) ^ [_135993, _135995] : [-(strict_implies(_135995, _135993) = necessarily(implies(_135995, _135993)))]]], (928 ^ _108838) ^ [] : [op_strict_equiv, 931 ^ _108838 : [(932 ^ _108838) ^ [_136142, _136144] : [-(strict_equiv(_136144, _136142) = and(strict_implies(_136144, _136142), strict_implies(_136142, _136144)))]]], (569 ^ _108838) ^ [] : [571 ^ _108838 : [(572 ^ _108838) ^ [] : [-(is_a_theorem(570 ^ []))], (574 ^ _108838) ^ [] : [is_a_theorem(necessarily(570 ^ []))]], -(necessitation)], (559 ^ _108838) ^ [] : [necessitation, 562 ^ _108838 : [(563 ^ _108838) ^ [_125887] : [is_a_theorem(_125887), -(is_a_theorem(necessarily(_125887)))]]], (592 ^ _108838) ^ [] : [595 ^ _108838 : [(596 ^ _108838) ^ [] : [-(is_a_theorem(593 ^ []))], (598 ^ _108838) ^ [] : [-(is_a_theorem(strict_implies(593 ^ [], 594 ^ [])))], (600 ^ _108838) ^ [] : [is_a_theorem(594 ^ [])]], -(modus_ponens_strict_implies)], (578 ^ _108838) ^ [] : [modus_ponens_strict_implies, 581 ^ _108838 : [(582 ^ _108838) ^ [_126387, _126389] : [-(is_a_theorem(_126387)), is_a_theorem(_126389), is_a_theorem(strict_implies(_126389, _126387))]]], (618 ^ _108838) ^ [] : [621 ^ _108838 : [(622 ^ _108838) ^ [] : [-(is_a_theorem(619 ^ []))], (624 ^ _108838) ^ [] : [-(is_a_theorem(620 ^ []))], (626 ^ _108838) ^ [] : [is_a_theorem(and(619 ^ [], 620 ^ []))]], -(adjunction)], (604 ^ _108838) ^ [] : [adjunction, 607 ^ _108838 : [(608 ^ _108838) ^ [_127097, _127099] : [-(is_a_theorem(and(_127099, _127097))), is_a_theorem(_127099), is_a_theorem(_127097)]]], (640 ^ _108838) ^ [] : [643 ^ _108838 : [(644 ^ _108838) ^ [] : [-(is_a_theorem(strict_equiv(641 ^ [], 642 ^ [])))], (646 ^ _108838) ^ [] : [641 ^ [] = 642 ^ []]], -(substitution_strict_equiv)], (630 ^ _108838) ^ [] : [substitution_strict_equiv, 633 ^ _108838 : [(634 ^ _108838) ^ [_127807, _127809] : [is_a_theorem(strict_equiv(_127809, _127807)), -(_127809 = _127807)]]], (650 ^ _108838) ^ [] : [axiom_K, 653 ^ _108838 : [(654 ^ _108838) ^ [_128354, _128356] : [-(is_a_theorem(implies(necessarily(implies(_128356, _128354)), implies(necessarily(_128356), necessarily(_128354)))))]]], (656 ^ _108838) ^ [] : [is_a_theorem(implies(necessarily(implies(657 ^ [], 658 ^ [])), implies(necessarily(657 ^ []), necessarily(658 ^ [])))), -(axiom_K)], (664 ^ _108838) ^ [] : [axiom_M, 667 ^ _108838 : [(668 ^ _108838) ^ [_128750] : [-(is_a_theorem(implies(necessarily(_128750), _128750)))]]], (670 ^ _108838) ^ [] : [is_a_theorem(implies(necessarily(671 ^ []), 671 ^ [])), -(axiom_M)], (677 ^ _108838) ^ [] : [axiom_4, 680 ^ _108838 : [(681 ^ _108838) ^ [_129070] : [-(is_a_theorem(implies(necessarily(_129070), necessarily(necessarily(_129070)))))]]], (683 ^ _108838) ^ [] : [is_a_theorem(implies(necessarily(684 ^ []), necessarily(necessarily(684 ^ [])))), -(axiom_4)], (690 ^ _108838) ^ [] : [axiom_B, 693 ^ _108838 : [(694 ^ _108838) ^ [_129398] : [-(is_a_theorem(implies(_129398, necessarily(possibly(_129398)))))]]], (696 ^ _108838) ^ [] : [is_a_theorem(implies(697 ^ [], necessarily(possibly(697 ^ [])))), -(axiom_B)], (703 ^ _108838) ^ [] : [axiom_5, 706 ^ _108838 : [(707 ^ _108838) ^ [_129722] : [-(is_a_theorem(implies(possibly(_129722), necessarily(possibly(_129722)))))]]], (709 ^ _108838) ^ [] : [is_a_theorem(implies(possibly(710 ^ []), necessarily(possibly(710 ^ [])))), -(axiom_5)], (716 ^ _108838) ^ [] : [axiom_s1, 719 ^ _108838 : [(720 ^ _108838) ^ [_130078, _130080, _130082] : [-(is_a_theorem(implies(and(necessarily(implies(_130082, _130080)), necessarily(implies(_130080, _130078))), necessarily(implies(_130082, _130078)))))]]], (722 ^ _108838) ^ [] : [is_a_theorem(implies(and(necessarily(implies(723 ^ [], 724 ^ [])), necessarily(implies(724 ^ [], 725 ^ []))), necessarily(implies(723 ^ [], 725 ^ [])))), -(axiom_s1)], (731 ^ _108838) ^ [] : [axiom_s2, 734 ^ _108838 : [(735 ^ _108838) ^ [_130572, _130574] : [-(is_a_theorem(strict_implies(possibly(and(_130574, _130572)), and(possibly(_130574), possibly(_130572)))))]]], (737 ^ _108838) ^ [] : [is_a_theorem(strict_implies(possibly(and(738 ^ [], 739 ^ [])), and(possibly(738 ^ []), possibly(739 ^ [])))), -(axiom_s2)], (745 ^ _108838) ^ [] : [axiom_s3, 748 ^ _108838 : [(749 ^ _108838) ^ [_130982, _130984] : [-(is_a_theorem(strict_implies(strict_implies(_130984, _130982), strict_implies(not possibly(_130982), not possibly(_130984)))))]]], (751 ^ _108838) ^ [] : [is_a_theorem(strict_implies(strict_implies(752 ^ [], 753 ^ []), strict_implies(not possibly(753 ^ []), not possibly(752 ^ [])))), -(axiom_s3)], (759 ^ _108838) ^ [] : [axiom_s4, 762 ^ _108838 : [(763 ^ _108838) ^ [_131382] : [-(is_a_theorem(strict_implies(necessarily(_131382), necessarily(necessarily(_131382)))))]]], (765 ^ _108838) ^ [] : [is_a_theorem(strict_implies(necessarily(766 ^ []), necessarily(necessarily(766 ^ [])))), -(axiom_s4)], (772 ^ _108838) ^ [] : [axiom_m1, 775 ^ _108838 : [(776 ^ _108838) ^ [_131724, _131726] : [-(is_a_theorem(strict_implies(and(_131726, _131724), and(_131724, _131726))))]]], (778 ^ _108838) ^ [] : [is_a_theorem(strict_implies(and(779 ^ [], 780 ^ []), and(780 ^ [], 779 ^ []))), -(axiom_m1)], (786 ^ _108838) ^ [] : [axiom_m2, 789 ^ _108838 : [(790 ^ _108838) ^ [_132118, _132120] : [-(is_a_theorem(strict_implies(and(_132120, _132118), _132120)))]]], (792 ^ _108838) ^ [] : [is_a_theorem(strict_implies(and(793 ^ [], 794 ^ []), 793 ^ [])), -(axiom_m2)], (800 ^ _108838) ^ [] : [axiom_m3, 803 ^ _108838 : [(804 ^ _108838) ^ [_132517, _132519, _132521] : [-(is_a_theorem(strict_implies(and(and(_132521, _132519), _132517), and(_132521, and(_132519, _132517)))))]]], (806 ^ _108838) ^ [] : [is_a_theorem(strict_implies(and(and(807 ^ [], 808 ^ []), 809 ^ []), and(807 ^ [], and(808 ^ [], 809 ^ [])))), -(axiom_m3)], (815 ^ _108838) ^ [] : [axiom_m4, 818 ^ _108838 : [(819 ^ _108838) ^ [_132975] : [-(is_a_theorem(strict_implies(_132975, and(_132975, _132975))))]]], (821 ^ _108838) ^ [] : [is_a_theorem(strict_implies(822 ^ [], and(822 ^ [], 822 ^ []))), -(axiom_m4)], (828 ^ _108838) ^ [] : [axiom_m5, 831 ^ _108838 : [(832 ^ _108838) ^ [_133325, _133327, _133329] : [-(is_a_theorem(strict_implies(and(strict_implies(_133329, _133327), strict_implies(_133327, _133325)), strict_implies(_133329, _133325))))]]], (834 ^ _108838) ^ [] : [is_a_theorem(strict_implies(and(strict_implies(835 ^ [], 836 ^ []), strict_implies(836 ^ [], 837 ^ [])), strict_implies(835 ^ [], 837 ^ []))), -(axiom_m5)], (843 ^ _108838) ^ [] : [axiom_m6, 846 ^ _108838 : [(847 ^ _108838) ^ [_133783] : [-(is_a_theorem(strict_implies(_133783, possibly(_133783))))]]], (849 ^ _108838) ^ [] : [is_a_theorem(strict_implies(850 ^ [], possibly(850 ^ []))), -(axiom_m6)], (856 ^ _108838) ^ [] : [axiom_m7, 859 ^ _108838 : [(860 ^ _108838) ^ [_134117, _134119] : [-(is_a_theorem(strict_implies(possibly(and(_134119, _134117)), _134119)))]]], (862 ^ _108838) ^ [] : [is_a_theorem(strict_implies(possibly(and(863 ^ [], 864 ^ [])), 863 ^ [])), -(axiom_m7)], (870 ^ _108838) ^ [] : [axiom_m8, 873 ^ _108838 : [(874 ^ _108838) ^ [_134508, _134510] : [-(is_a_theorem(strict_implies(strict_implies(_134510, _134508), strict_implies(possibly(_134510), possibly(_134508)))))]]], (876 ^ _108838) ^ [] : [is_a_theorem(strict_implies(strict_implies(877 ^ [], 878 ^ []), strict_implies(possibly(877 ^ []), possibly(878 ^ [])))), -(axiom_m8)], (884 ^ _108838) ^ [] : [axiom_m9, 887 ^ _108838 : [(888 ^ _108838) ^ [_134898] : [-(is_a_theorem(strict_implies(possibly(possibly(_134898)), possibly(_134898))))]]], (890 ^ _108838) ^ [] : [is_a_theorem(strict_implies(possibly(possibly(891 ^ [])), possibly(891 ^ []))), -(axiom_m9)], (897 ^ _108838) ^ [] : [axiom_m10, 900 ^ _108838 : [(901 ^ _108838) ^ [_135206] : [-(is_a_theorem(strict_implies(possibly(_135206), necessarily(possibly(_135206)))))]]], (903 ^ _108838) ^ [] : [is_a_theorem(strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))), -(axiom_m10)]], input).
% 15.00/14.82  ncf('1',plain,[axiom_m4],start(956 ^ 0)).
% 15.00/14.82  ncf('1.1',plain,[-(axiom_m4), is_a_theorem(strict_implies(822 ^ [], and(822 ^ [], 822 ^ [])))],extension(821 ^ 1)).
% 15.00/14.82  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([[_109586, _109588], [strict_implies(822 ^ [], and(822 ^ [], 822 ^ [])), necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ [])))]]))).
% 15.00/14.82  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([[_109089, _109091], [necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))), strict_implies(822 ^ [], and(822 ^ [], 822 ^ []))]]))).
% 15.00/14.82  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([[_109293, _109295, _109297], [necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))), necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))), strict_implies(822 ^ [], and(822 ^ [], 822 ^ []))]]))).
% 15.00/14.82  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([[_135993, _135995], [and(822 ^ [], 822 ^ []), 822 ^ []]]))).
% 15.00/14.82  ncf('1.1.1.1.1.1.1',plain,[-(op_strict_implies)],extension(950 ^ 6)).
% 15.00/14.82  ncf('1.1.1.1.1.2',plain,[-(necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))) = necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ []))))],extension(2 ^ 5,bind([[_108982], [necessarily(implies(822 ^ [], and(822 ^ [], 822 ^ [])))]]))).
% 15.00/14.82  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([[_125887], [implies(822 ^ [], and(822 ^ [], 822 ^ []))]]))).
% 15.00/14.82  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([[_112806, _112808], [implies(822 ^ [], and(822 ^ [], 822 ^ [])), implies(822 ^ [], implies(822 ^ [], and(822 ^ [], 822 ^ [])))]]))).
% 15.00/14.82  ncf('1.1.1.2.1.1',plain,[-(is_a_theorem(implies(822 ^ [], implies(822 ^ [], and(822 ^ [], 822 ^ []))))), and_3],extension(239 ^ 9,bind([[_116511, _116513], [822 ^ [], 822 ^ []]]))).
% 15.00/14.82  ncf('1.1.1.2.1.1.1',plain,[-(and_3)],extension(543 ^ 10)).
% 15.00/14.82  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([[_114852, _114854], [and(822 ^ [], 822 ^ []), 822 ^ []]]))).
% 15.00/14.82  ncf('1.1.1.2.1.2.1',plain,[-(implies_2)],extension(535 ^ 10)).
% 15.00/14.82  ncf('1.1.1.2.1.3',plain,[-(modus_ponens)],extension(529 ^ 7)).
% 15.00/14.82  ncf('1.1.1.2.2',plain,[-(necessitation)],extension(936 ^ 4)).
% 15.00/14.82  %-----------------------------------------------------
% 15.00/14.82  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------