%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL536+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n007.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 0.66s 1.38s
% Output   : Proof 0.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL536+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n007.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 16:10:38 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.66/1.38  
% 0.66/1.38  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.66/1.38  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.66/1.38  %-----------------------------------------------------
% 0.66/1.38  ncf(matrix, plain, [(956 ^ _107907) ^ [] : [axiom_m10], (20 ^ _107907) ^ [_108655, _108657] : [-(is_a_theorem(_108655)), _108657 = _108655, is_a_theorem(_108657)], (2 ^ _107907) ^ [_108051] : [-(_108051 = _108051)], (4 ^ _107907) ^ [_108158, _108160] : [_108160 = _108158, -(_108158 = _108160)], (10 ^ _107907) ^ [_108362, _108364, _108366] : [-(_108366 = _108362), _108366 = _108364, _108364 = _108362], (30 ^ _107907) ^ [_108980, _108982, _108984, _108986] : [-(or(_108986, _108982) = or(_108984, _108980)), _108986 = _108984, _108982 = _108980], (40 ^ _107907) ^ [_109339, _109341, _109343, _109345] : [-(equiv(_109345, _109341) = equiv(_109343, _109339)), _109345 = _109343, _109341 = _109339], (50 ^ _107907) ^ [_109670, _109672] : [_109672 = _109670, -(possibly(_109672) = possibly(_109670))], (56 ^ _107907) ^ [_109888, _109890] : [_109890 = _109888, -((not _109890) = (not _109888))], (62 ^ _107907) ^ [_110106, _110108] : [_110108 = _110106, -(necessarily(_110108) = necessarily(_110106))], (68 ^ _107907) ^ [_110352, _110354, _110356, _110358] : [-(implies(_110358, _110354) = implies(_110356, _110352)), _110358 = _110356, _110354 = _110352], (78 ^ _107907) ^ [_110711, _110713, _110715, _110717] : [-(strict_equiv(_110717, _110713) = strict_equiv(_110715, _110711)), _110717 = _110715, _110713 = _110711], (88 ^ _107907) ^ [_111070, _111072, _111074, _111076] : [-(and(_111076, _111072) = and(_111074, _111070)), _111076 = _111074, _111072 = _111070], (98 ^ _107907) ^ [_111409, _111411, _111413, _111415] : [-(strict_implies(_111415, _111411) = strict_implies(_111413, _111409)), _111415 = _111413, _111411 = _111409], (122 ^ _107907) ^ [] : [125 ^ _107907 : [(126 ^ _107907) ^ [] : [-(is_a_theorem(123 ^ []))], (128 ^ _107907) ^ [] : [-(is_a_theorem(implies(123 ^ [], 124 ^ [])))], (130 ^ _107907) ^ [] : [is_a_theorem(124 ^ [])]], -(modus_ponens)], (108 ^ _107907) ^ [] : [modus_ponens, 111 ^ _107907 : [(112 ^ _107907) ^ [_111875, _111877] : [-(is_a_theorem(_111875)), is_a_theorem(_111877), is_a_theorem(implies(_111877, _111875))]]], (144 ^ _107907) ^ [] : [147 ^ _107907 : [(148 ^ _107907) ^ [] : [-(is_a_theorem(equiv(145 ^ [], 146 ^ [])))], (150 ^ _107907) ^ [] : [145 ^ [] = 146 ^ []]], -(substitution_of_equivalents)], (134 ^ _107907) ^ [] : [substitution_of_equivalents, 137 ^ _107907 : [(138 ^ _107907) ^ [_112585, _112587] : [is_a_theorem(equiv(_112587, _112585)), -(_112587 = _112585)]]], (154 ^ _107907) ^ [] : [modus_tollens, 157 ^ _107907 : [(158 ^ _107907) ^ [_113132, _113134] : [-(is_a_theorem(implies(implies(not _113132, not _113134), implies(_113134, _113132))))]]], (160 ^ _107907) ^ [] : [is_a_theorem(implies(implies(not 162 ^ [], not 161 ^ []), implies(161 ^ [], 162 ^ []))), -(modus_tollens)], (168 ^ _107907) ^ [] : [implies_1, 171 ^ _107907 : [(172 ^ _107907) ^ [_113536, _113538] : [-(is_a_theorem(implies(_113538, implies(_113536, _113538))))]]], (174 ^ _107907) ^ [] : [is_a_theorem(implies(175 ^ [], implies(176 ^ [], 175 ^ []))), -(implies_1)], (182 ^ _107907) ^ [] : [implies_2, 185 ^ _107907 : [(186 ^ _107907) ^ [_113921, _113923] : [-(is_a_theorem(implies(implies(_113923, implies(_113923, _113921)), implies(_113923, _113921))))]]], (188 ^ _107907) ^ [] : [is_a_theorem(implies(implies(189 ^ [], implies(189 ^ [], 190 ^ [])), implies(189 ^ [], 190 ^ []))), -(implies_2)], (196 ^ _107907) ^ [] : [implies_3, 199 ^ _107907 : [(200 ^ _107907) ^ [_114338, _114340, _114342] : [-(is_a_theorem(implies(implies(_114342, _114340), implies(implies(_114340, _114338), implies(_114342, _114338)))))]]], (202 ^ _107907) ^ [] : [is_a_theorem(implies(implies(203 ^ [], 204 ^ []), implies(implies(204 ^ [], 205 ^ []), implies(203 ^ [], 205 ^ [])))), -(implies_3)], (211 ^ _107907) ^ [] : [and_1, 214 ^ _107907 : [(215 ^ _107907) ^ [_114810, _114812] : [-(is_a_theorem(implies(and(_114812, _114810), _114812)))]]], (217 ^ _107907) ^ [] : [is_a_theorem(implies(and(218 ^ [], 219 ^ []), 218 ^ [])), -(and_1)], (225 ^ _107907) ^ [] : [and_2, 228 ^ _107907 : [(229 ^ _107907) ^ [_115195, _115197] : [-(is_a_theorem(implies(and(_115197, _115195), _115195)))]]], (231 ^ _107907) ^ [] : [is_a_theorem(implies(and(232 ^ [], 233 ^ []), 233 ^ [])), -(and_2)], (239 ^ _107907) ^ [] : [and_3, 242 ^ _107907 : [(243 ^ _107907) ^ [_115580, _115582] : [-(is_a_theorem(implies(_115582, implies(_115580, and(_115582, _115580)))))]]], (245 ^ _107907) ^ [] : [is_a_theorem(implies(246 ^ [], implies(247 ^ [], and(246 ^ [], 247 ^ [])))), -(and_3)], (253 ^ _107907) ^ [] : [or_1, 256 ^ _107907 : [(257 ^ _107907) ^ [_115974, _115976] : [-(is_a_theorem(implies(_115976, or(_115976, _115974))))]]], (259 ^ _107907) ^ [] : [is_a_theorem(implies(260 ^ [], or(260 ^ [], 261 ^ []))), -(or_1)], (267 ^ _107907) ^ [] : [or_2, 270 ^ _107907 : [(271 ^ _107907) ^ [_116359, _116361] : [-(is_a_theorem(implies(_116359, or(_116361, _116359))))]]], (273 ^ _107907) ^ [] : [is_a_theorem(implies(275 ^ [], or(274 ^ [], 275 ^ []))), -(or_2)], (281 ^ _107907) ^ [] : [or_3, 284 ^ _107907 : [(285 ^ _107907) ^ [_116758, _116760, _116762] : [-(is_a_theorem(implies(implies(_116762, _116758), implies(implies(_116760, _116758), implies(or(_116762, _116760), _116758)))))]]], (287 ^ _107907) ^ [] : [is_a_theorem(implies(implies(288 ^ [], 290 ^ []), implies(implies(289 ^ [], 290 ^ []), implies(or(288 ^ [], 289 ^ []), 290 ^ [])))), -(or_3)], (296 ^ _107907) ^ [] : [equivalence_1, 299 ^ _107907 : [(300 ^ _107907) ^ [_117242, _117244] : [-(is_a_theorem(implies(equiv(_117244, _117242), implies(_117244, _117242))))]]], (302 ^ _107907) ^ [] : [is_a_theorem(implies(equiv(303 ^ [], 304 ^ []), implies(303 ^ [], 304 ^ []))), -(equivalence_1)], (310 ^ _107907) ^ [] : [equivalence_2, 313 ^ _107907 : [(314 ^ _107907) ^ [_117636, _117638] : [-(is_a_theorem(implies(equiv(_117638, _117636), implies(_117636, _117638))))]]], (316 ^ _107907) ^ [] : [is_a_theorem(implies(equiv(317 ^ [], 318 ^ []), implies(318 ^ [], 317 ^ []))), -(equivalence_2)], (324 ^ _107907) ^ [] : [equivalence_3, 327 ^ _107907 : [(328 ^ _107907) ^ [_118030, _118032] : [-(is_a_theorem(implies(implies(_118032, _118030), implies(implies(_118030, _118032), equiv(_118032, _118030)))))]]], (330 ^ _107907) ^ [] : [is_a_theorem(implies(implies(331 ^ [], 332 ^ []), implies(implies(332 ^ [], 331 ^ []), equiv(331 ^ [], 332 ^ [])))), -(equivalence_3)], (338 ^ _107907) ^ [] : [kn1, 341 ^ _107907 : [(342 ^ _107907) ^ [_118428] : [-(is_a_theorem(implies(_118428, and(_118428, _118428))))]]], (344 ^ _107907) ^ [] : [is_a_theorem(implies(345 ^ [], and(345 ^ [], 345 ^ []))), -(kn1)], (351 ^ _107907) ^ [] : [kn2, 354 ^ _107907 : [(355 ^ _107907) ^ [_118764, _118766] : [-(is_a_theorem(implies(and(_118766, _118764), _118766)))]]], (357 ^ _107907) ^ [] : [is_a_theorem(implies(and(358 ^ [], 359 ^ []), 358 ^ [])), -(kn2)], (365 ^ _107907) ^ [] : [kn3, 368 ^ _107907 : [(369 ^ _107907) ^ [_119163, _119165, _119167] : [-(is_a_theorem(implies(implies(_119167, _119165), implies(not and(_119165, _119163), not and(_119163, _119167)))))]]], (371 ^ _107907) ^ [] : [is_a_theorem(implies(implies(372 ^ [], 373 ^ []), implies(not and(373 ^ [], 374 ^ []), not and(374 ^ [], 372 ^ [])))), -(kn3)], (380 ^ _107907) ^ [] : [cn1, 383 ^ _107907 : [(384 ^ _107907) ^ [_119665, _119667, _119669] : [-(is_a_theorem(implies(implies(_119669, _119667), implies(implies(_119667, _119665), implies(_119669, _119665)))))]]], (386 ^ _107907) ^ [] : [is_a_theorem(implies(implies(387 ^ [], 388 ^ []), implies(implies(388 ^ [], 389 ^ []), implies(387 ^ [], 389 ^ [])))), -(cn1)], (395 ^ _107907) ^ [] : [cn2, 398 ^ _107907 : [(399 ^ _107907) ^ [_120137, _120139] : [-(is_a_theorem(implies(_120139, implies(not _120139, _120137))))]]], (401 ^ _107907) ^ [] : [is_a_theorem(implies(402 ^ [], implies(not 402 ^ [], 403 ^ []))), -(cn2)], (409 ^ _107907) ^ [] : [cn3, 412 ^ _107907 : [(413 ^ _107907) ^ [_120512] : [-(is_a_theorem(implies(implies(not _120512, _120512), _120512)))]]], (415 ^ _107907) ^ [] : [is_a_theorem(implies(implies(not 416 ^ [], 416 ^ []), 416 ^ [])), -(cn3)], (422 ^ _107907) ^ [] : [r1, 425 ^ _107907 : [(426 ^ _107907) ^ [_120838] : [-(is_a_theorem(implies(or(_120838, _120838), _120838)))]]], (428 ^ _107907) ^ [] : [is_a_theorem(implies(or(429 ^ [], 429 ^ []), 429 ^ [])), -(r1)], (435 ^ _107907) ^ [] : [r2, 438 ^ _107907 : [(439 ^ _107907) ^ [_121174, _121176] : [-(is_a_theorem(implies(_121174, or(_121176, _121174))))]]], (441 ^ _107907) ^ [] : [is_a_theorem(implies(443 ^ [], or(442 ^ [], 443 ^ []))), -(r2)], (449 ^ _107907) ^ [] : [r3, 452 ^ _107907 : [(453 ^ _107907) ^ [_121559, _121561] : [-(is_a_theorem(implies(or(_121561, _121559), or(_121559, _121561))))]]], (455 ^ _107907) ^ [] : [is_a_theorem(implies(or(456 ^ [], 457 ^ []), or(457 ^ [], 456 ^ []))), -(r3)], (463 ^ _107907) ^ [] : [r4, 466 ^ _107907 : [(467 ^ _107907) ^ [_121967, _121969, _121971] : [-(is_a_theorem(implies(or(_121971, or(_121969, _121967)), or(_121969, or(_121971, _121967)))))]]], (469 ^ _107907) ^ [] : [is_a_theorem(implies(or(470 ^ [], or(471 ^ [], 472 ^ [])), or(471 ^ [], or(470 ^ [], 472 ^ [])))), -(r4)], (478 ^ _107907) ^ [] : [r5, 481 ^ _107907 : [(482 ^ _107907) ^ [_122436, _122438, _122440] : [-(is_a_theorem(implies(implies(_122438, _122436), implies(or(_122440, _122438), or(_122440, _122436)))))]]], (484 ^ _107907) ^ [] : [is_a_theorem(implies(implies(486 ^ [], 487 ^ []), implies(or(485 ^ [], 486 ^ []), or(485 ^ [], 487 ^ [])))), -(r5)], (493 ^ _107907) ^ [] : [op_or, 496 ^ _107907 : [(497 ^ _107907) ^ [_123071, _123073] : [-(or(_123073, _123071) = (not and(not _123073, not _123071)))]]], (499 ^ _107907) ^ [] : [op_and, 502 ^ _107907 : [(503 ^ _107907) ^ [_123244, _123246] : [-(and(_123246, _123244) = (not or(not _123246, not _123244)))]]], (505 ^ _107907) ^ [] : [op_implies_and, 508 ^ _107907 : [(509 ^ _107907) ^ [_123417, _123419] : [-(implies(_123419, _123417) = (not and(_123419, not _123417)))]]], (511 ^ _107907) ^ [] : [op_implies_or, 514 ^ _107907 : [(515 ^ _107907) ^ [_123588, _123590] : [-(implies(_123590, _123588) = or(not _123590, _123588))]]], (517 ^ _107907) ^ [] : [op_equiv, 520 ^ _107907 : [(521 ^ _107907) ^ [_123737, _123739] : [-(equiv(_123739, _123737) = and(implies(_123739, _123737), implies(_123737, _123739)))]]], (523 ^ _107907) ^ [] : [-(op_or)], (525 ^ _107907) ^ [] : [-(op_implies_and)], (527 ^ _107907) ^ [] : [-(op_equiv)], (529 ^ _107907) ^ [] : [-(modus_ponens)], (531 ^ _107907) ^ [] : [-(modus_tollens)], (533 ^ _107907) ^ [] : [-(implies_1)], (535 ^ _107907) ^ [] : [-(implies_2)], (537 ^ _107907) ^ [] : [-(implies_3)], (539 ^ _107907) ^ [] : [-(and_1)], (541 ^ _107907) ^ [] : [-(and_2)], (543 ^ _107907) ^ [] : [-(and_3)], (545 ^ _107907) ^ [] : [-(or_1)], (547 ^ _107907) ^ [] : [-(or_2)], (549 ^ _107907) ^ [] : [-(or_3)], (551 ^ _107907) ^ [] : [-(equivalence_1)], (553 ^ _107907) ^ [] : [-(equivalence_2)], (555 ^ _107907) ^ [] : [-(equivalence_3)], (557 ^ _107907) ^ [] : [-(substitution_of_equivalents)], (934 ^ _107907) ^ [] : [-(op_possibly)], (936 ^ _107907) ^ [] : [-(necessitation)], (938 ^ _107907) ^ [] : [-(axiom_K)], (940 ^ _107907) ^ [] : [-(axiom_M)], (942 ^ _107907) ^ [] : [-(axiom_5)], (944 ^ _107907) ^ [] : [-(op_possibly)], (946 ^ _107907) ^ [] : [-(op_or)], (948 ^ _107907) ^ [] : [-(op_implies)], (950 ^ _107907) ^ [] : [-(op_strict_implies)], (952 ^ _107907) ^ [] : [-(op_equiv)], (954 ^ _107907) ^ [] : [-(op_strict_equiv)], (910 ^ _107907) ^ [] : [op_possibly, 913 ^ _107907 : [(914 ^ _107907) ^ [_134742] : [-(possibly(_134742) = (not necessarily(not _134742)))]]], (916 ^ _107907) ^ [] : [op_necessarily, 919 ^ _107907 : [(920 ^ _107907) ^ [_134895] : [-(necessarily(_134895) = (not possibly(not _134895)))]]], (922 ^ _107907) ^ [] : [op_strict_implies, 925 ^ _107907 : [(926 ^ _107907) ^ [_135062, _135064] : [-(strict_implies(_135064, _135062) = necessarily(implies(_135064, _135062)))]]], (928 ^ _107907) ^ [] : [op_strict_equiv, 931 ^ _107907 : [(932 ^ _107907) ^ [_135211, _135213] : [-(strict_equiv(_135213, _135211) = and(strict_implies(_135213, _135211), strict_implies(_135211, _135213)))]]], (569 ^ _107907) ^ [] : [571 ^ _107907 : [(572 ^ _107907) ^ [] : [-(is_a_theorem(570 ^ []))], (574 ^ _107907) ^ [] : [is_a_theorem(necessarily(570 ^ []))]], -(necessitation)], (559 ^ _107907) ^ [] : [necessitation, 562 ^ _107907 : [(563 ^ _107907) ^ [_124956] : [is_a_theorem(_124956), -(is_a_theorem(necessarily(_124956)))]]], (592 ^ _107907) ^ [] : [595 ^ _107907 : [(596 ^ _107907) ^ [] : [-(is_a_theorem(593 ^ []))], (598 ^ _107907) ^ [] : [-(is_a_theorem(strict_implies(593 ^ [], 594 ^ [])))], (600 ^ _107907) ^ [] : [is_a_theorem(594 ^ [])]], -(modus_ponens_strict_implies)], (578 ^ _107907) ^ [] : [modus_ponens_strict_implies, 581 ^ _107907 : [(582 ^ _107907) ^ [_125456, _125458] : [-(is_a_theorem(_125456)), is_a_theorem(_125458), is_a_theorem(strict_implies(_125458, _125456))]]], (618 ^ _107907) ^ [] : [621 ^ _107907 : [(622 ^ _107907) ^ [] : [-(is_a_theorem(619 ^ []))], (624 ^ _107907) ^ [] : [-(is_a_theorem(620 ^ []))], (626 ^ _107907) ^ [] : [is_a_theorem(and(619 ^ [], 620 ^ []))]], -(adjunction)], (604 ^ _107907) ^ [] : [adjunction, 607 ^ _107907 : [(608 ^ _107907) ^ [_126166, _126168] : [-(is_a_theorem(and(_126168, _126166))), is_a_theorem(_126168), is_a_theorem(_126166)]]], (640 ^ _107907) ^ [] : [643 ^ _107907 : [(644 ^ _107907) ^ [] : [-(is_a_theorem(strict_equiv(641 ^ [], 642 ^ [])))], (646 ^ _107907) ^ [] : [641 ^ [] = 642 ^ []]], -(substitution_strict_equiv)], (630 ^ _107907) ^ [] : [substitution_strict_equiv, 633 ^ _107907 : [(634 ^ _107907) ^ [_126876, _126878] : [is_a_theorem(strict_equiv(_126878, _126876)), -(_126878 = _126876)]]], (650 ^ _107907) ^ [] : [axiom_K, 653 ^ _107907 : [(654 ^ _107907) ^ [_127423, _127425] : [-(is_a_theorem(implies(necessarily(implies(_127425, _127423)), implies(necessarily(_127425), necessarily(_127423)))))]]], (656 ^ _107907) ^ [] : [is_a_theorem(implies(necessarily(implies(657 ^ [], 658 ^ [])), implies(necessarily(657 ^ []), necessarily(658 ^ [])))), -(axiom_K)], (664 ^ _107907) ^ [] : [axiom_M, 667 ^ _107907 : [(668 ^ _107907) ^ [_127819] : [-(is_a_theorem(implies(necessarily(_127819), _127819)))]]], (670 ^ _107907) ^ [] : [is_a_theorem(implies(necessarily(671 ^ []), 671 ^ [])), -(axiom_M)], (677 ^ _107907) ^ [] : [axiom_4, 680 ^ _107907 : [(681 ^ _107907) ^ [_128139] : [-(is_a_theorem(implies(necessarily(_128139), necessarily(necessarily(_128139)))))]]], (683 ^ _107907) ^ [] : [is_a_theorem(implies(necessarily(684 ^ []), necessarily(necessarily(684 ^ [])))), -(axiom_4)], (690 ^ _107907) ^ [] : [axiom_B, 693 ^ _107907 : [(694 ^ _107907) ^ [_128467] : [-(is_a_theorem(implies(_128467, necessarily(possibly(_128467)))))]]], (696 ^ _107907) ^ [] : [is_a_theorem(implies(697 ^ [], necessarily(possibly(697 ^ [])))), -(axiom_B)], (703 ^ _107907) ^ [] : [axiom_5, 706 ^ _107907 : [(707 ^ _107907) ^ [_128791] : [-(is_a_theorem(implies(possibly(_128791), necessarily(possibly(_128791)))))]]], (709 ^ _107907) ^ [] : [is_a_theorem(implies(possibly(710 ^ []), necessarily(possibly(710 ^ [])))), -(axiom_5)], (716 ^ _107907) ^ [] : [axiom_s1, 719 ^ _107907 : [(720 ^ _107907) ^ [_129147, _129149, _129151] : [-(is_a_theorem(implies(and(necessarily(implies(_129151, _129149)), necessarily(implies(_129149, _129147))), necessarily(implies(_129151, _129147)))))]]], (722 ^ _107907) ^ [] : [is_a_theorem(implies(and(necessarily(implies(723 ^ [], 724 ^ [])), necessarily(implies(724 ^ [], 725 ^ []))), necessarily(implies(723 ^ [], 725 ^ [])))), -(axiom_s1)], (731 ^ _107907) ^ [] : [axiom_s2, 734 ^ _107907 : [(735 ^ _107907) ^ [_129641, _129643] : [-(is_a_theorem(strict_implies(possibly(and(_129643, _129641)), and(possibly(_129643), possibly(_129641)))))]]], (737 ^ _107907) ^ [] : [is_a_theorem(strict_implies(possibly(and(738 ^ [], 739 ^ [])), and(possibly(738 ^ []), possibly(739 ^ [])))), -(axiom_s2)], (745 ^ _107907) ^ [] : [axiom_s3, 748 ^ _107907 : [(749 ^ _107907) ^ [_130051, _130053] : [-(is_a_theorem(strict_implies(strict_implies(_130053, _130051), strict_implies(not possibly(_130051), not possibly(_130053)))))]]], (751 ^ _107907) ^ [] : [is_a_theorem(strict_implies(strict_implies(752 ^ [], 753 ^ []), strict_implies(not possibly(753 ^ []), not possibly(752 ^ [])))), -(axiom_s3)], (759 ^ _107907) ^ [] : [axiom_s4, 762 ^ _107907 : [(763 ^ _107907) ^ [_130451] : [-(is_a_theorem(strict_implies(necessarily(_130451), necessarily(necessarily(_130451)))))]]], (765 ^ _107907) ^ [] : [is_a_theorem(strict_implies(necessarily(766 ^ []), necessarily(necessarily(766 ^ [])))), -(axiom_s4)], (772 ^ _107907) ^ [] : [axiom_m1, 775 ^ _107907 : [(776 ^ _107907) ^ [_130793, _130795] : [-(is_a_theorem(strict_implies(and(_130795, _130793), and(_130793, _130795))))]]], (778 ^ _107907) ^ [] : [is_a_theorem(strict_implies(and(779 ^ [], 780 ^ []), and(780 ^ [], 779 ^ []))), -(axiom_m1)], (786 ^ _107907) ^ [] : [axiom_m2, 789 ^ _107907 : [(790 ^ _107907) ^ [_131187, _131189] : [-(is_a_theorem(strict_implies(and(_131189, _131187), _131189)))]]], (792 ^ _107907) ^ [] : [is_a_theorem(strict_implies(and(793 ^ [], 794 ^ []), 793 ^ [])), -(axiom_m2)], (800 ^ _107907) ^ [] : [axiom_m3, 803 ^ _107907 : [(804 ^ _107907) ^ [_131586, _131588, _131590] : [-(is_a_theorem(strict_implies(and(and(_131590, _131588), _131586), and(_131590, and(_131588, _131586)))))]]], (806 ^ _107907) ^ [] : [is_a_theorem(strict_implies(and(and(807 ^ [], 808 ^ []), 809 ^ []), and(807 ^ [], and(808 ^ [], 809 ^ [])))), -(axiom_m3)], (815 ^ _107907) ^ [] : [axiom_m4, 818 ^ _107907 : [(819 ^ _107907) ^ [_132044] : [-(is_a_theorem(strict_implies(_132044, and(_132044, _132044))))]]], (821 ^ _107907) ^ [] : [is_a_theorem(strict_implies(822 ^ [], and(822 ^ [], 822 ^ []))), -(axiom_m4)], (828 ^ _107907) ^ [] : [axiom_m5, 831 ^ _107907 : [(832 ^ _107907) ^ [_132394, _132396, _132398] : [-(is_a_theorem(strict_implies(and(strict_implies(_132398, _132396), strict_implies(_132396, _132394)), strict_implies(_132398, _132394))))]]], (834 ^ _107907) ^ [] : [is_a_theorem(strict_implies(and(strict_implies(835 ^ [], 836 ^ []), strict_implies(836 ^ [], 837 ^ [])), strict_implies(835 ^ [], 837 ^ []))), -(axiom_m5)], (843 ^ _107907) ^ [] : [axiom_m6, 846 ^ _107907 : [(847 ^ _107907) ^ [_132852] : [-(is_a_theorem(strict_implies(_132852, possibly(_132852))))]]], (849 ^ _107907) ^ [] : [is_a_theorem(strict_implies(850 ^ [], possibly(850 ^ []))), -(axiom_m6)], (856 ^ _107907) ^ [] : [axiom_m7, 859 ^ _107907 : [(860 ^ _107907) ^ [_133186, _133188] : [-(is_a_theorem(strict_implies(possibly(and(_133188, _133186)), _133188)))]]], (862 ^ _107907) ^ [] : [is_a_theorem(strict_implies(possibly(and(863 ^ [], 864 ^ [])), 863 ^ [])), -(axiom_m7)], (870 ^ _107907) ^ [] : [axiom_m8, 873 ^ _107907 : [(874 ^ _107907) ^ [_133577, _133579] : [-(is_a_theorem(strict_implies(strict_implies(_133579, _133577), strict_implies(possibly(_133579), possibly(_133577)))))]]], (876 ^ _107907) ^ [] : [is_a_theorem(strict_implies(strict_implies(877 ^ [], 878 ^ []), strict_implies(possibly(877 ^ []), possibly(878 ^ [])))), -(axiom_m8)], (884 ^ _107907) ^ [] : [axiom_m9, 887 ^ _107907 : [(888 ^ _107907) ^ [_133967] : [-(is_a_theorem(strict_implies(possibly(possibly(_133967)), possibly(_133967))))]]], (890 ^ _107907) ^ [] : [is_a_theorem(strict_implies(possibly(possibly(891 ^ [])), possibly(891 ^ []))), -(axiom_m9)], (897 ^ _107907) ^ [] : [axiom_m10, 900 ^ _107907 : [(901 ^ _107907) ^ [_134275] : [-(is_a_theorem(strict_implies(possibly(_134275), necessarily(possibly(_134275)))))]]], (903 ^ _107907) ^ [] : [is_a_theorem(strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))), -(axiom_m10)]], input).
% 0.66/1.38  ncf('1',plain,[axiom_m10],start(956 ^ 0)).
% 0.66/1.38  ncf('1.1',plain,[-(axiom_m10), is_a_theorem(strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ []))))],extension(903 ^ 1)).
% 0.66/1.38  ncf('1.1.1',plain,[-(is_a_theorem(strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ []))))), necessarily(implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))) = strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ []))), is_a_theorem(necessarily(implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))))],extension(20 ^ 2,bind([[_108655, _108657], [strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ []))), necessarily(implies(possibly(904 ^ []), necessarily(possibly(904 ^ []))))]]))).
% 0.66/1.38  ncf('1.1.1.1',plain,[-(necessarily(implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))) = strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))), strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ []))) = necessarily(implies(possibly(904 ^ []), necessarily(possibly(904 ^ []))))],extension(4 ^ 3,bind([[_108158, _108160], [necessarily(implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))), strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))]]))).
% 0.66/1.38  ncf('1.1.1.1.1',plain,[-(strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ []))) = necessarily(implies(possibly(904 ^ []), necessarily(possibly(904 ^ []))))), op_strict_implies],extension(922 ^ 4,bind([[_135062, _135064], [necessarily(possibly(904 ^ [])), possibly(904 ^ [])]]))).
% 0.66/1.38  ncf('1.1.1.1.1.1',plain,[-(op_strict_implies)],extension(950 ^ 5)).
% 0.66/1.38  ncf('1.1.1.2',plain,[-(is_a_theorem(necessarily(implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))))), 563 : is_a_theorem(implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))), 563 : necessitation],extension(559 ^ 3,bind([[_124956], [implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))]]))).
% 0.66/1.38  ncf('1.1.1.2.1',plain,[-(is_a_theorem(implies(possibly(904 ^ []), necessarily(possibly(904 ^ []))))), axiom_5],extension(703 ^ 6,bind([[_128791], [904 ^ []]]))).
% 0.66/1.38  ncf('1.1.1.2.1.1',plain,[-(axiom_5)],extension(942 ^ 7)).
% 0.66/1.38  ncf('1.1.1.2.2',plain,[-(necessitation)],extension(936 ^ 4)).
% 0.66/1.38  %-----------------------------------------------------
% 0.66/1.38  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------