%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : LCL538+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n020.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 25.19s 25.26s
% Output   : Proof 25.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL538+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 16:27:32 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 25.19/25.26  
% 25.19/25.26  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 25.19/25.26  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.19/25.26  %-----------------------------------------------------
% 25.19/25.26  ncf(matrix, plain, [(958 ^ _109216) ^ [] : [modus_ponens_strict_implies], (20 ^ _109216) ^ [_109964, _109966] : [-(is_a_theorem(_109964)), _109966 = _109964, is_a_theorem(_109966)], (2 ^ _109216) ^ [_109360] : [-(_109360 = _109360)], (4 ^ _109216) ^ [_109467, _109469] : [_109469 = _109467, -(_109467 = _109469)], (10 ^ _109216) ^ [_109671, _109673, _109675] : [-(_109675 = _109671), _109675 = _109673, _109673 = _109671], (30 ^ _109216) ^ [_110289, _110291, _110293, _110295] : [-(or(_110295, _110291) = or(_110293, _110289)), _110295 = _110293, _110291 = _110289], (40 ^ _109216) ^ [_110648, _110650, _110652, _110654] : [-(equiv(_110654, _110650) = equiv(_110652, _110648)), _110654 = _110652, _110650 = _110648], (50 ^ _109216) ^ [_110979, _110981] : [_110981 = _110979, -(possibly(_110981) = possibly(_110979))], (56 ^ _109216) ^ [_111197, _111199] : [_111199 = _111197, -((not _111199) = (not _111197))], (62 ^ _109216) ^ [_111415, _111417] : [_111417 = _111415, -(necessarily(_111417) = necessarily(_111415))], (68 ^ _109216) ^ [_111661, _111663, _111665, _111667] : [-(implies(_111667, _111663) = implies(_111665, _111661)), _111667 = _111665, _111663 = _111661], (78 ^ _109216) ^ [_112020, _112022, _112024, _112026] : [-(strict_equiv(_112026, _112022) = strict_equiv(_112024, _112020)), _112026 = _112024, _112022 = _112020], (88 ^ _109216) ^ [_112379, _112381, _112383, _112385] : [-(and(_112385, _112381) = and(_112383, _112379)), _112385 = _112383, _112381 = _112379], (98 ^ _109216) ^ [_112718, _112720, _112722, _112724] : [-(strict_implies(_112724, _112720) = strict_implies(_112722, _112718)), _112724 = _112722, _112720 = _112718], (122 ^ _109216) ^ [] : [125 ^ _109216 : [(126 ^ _109216) ^ [] : [-(is_a_theorem(123 ^ []))], (128 ^ _109216) ^ [] : [-(is_a_theorem(implies(123 ^ [], 124 ^ [])))], (130 ^ _109216) ^ [] : [is_a_theorem(124 ^ [])]], -(modus_ponens)], (108 ^ _109216) ^ [] : [modus_ponens, 111 ^ _109216 : [(112 ^ _109216) ^ [_113184, _113186] : [-(is_a_theorem(_113184)), is_a_theorem(_113186), is_a_theorem(implies(_113186, _113184))]]], (144 ^ _109216) ^ [] : [147 ^ _109216 : [(148 ^ _109216) ^ [] : [-(is_a_theorem(equiv(145 ^ [], 146 ^ [])))], (150 ^ _109216) ^ [] : [145 ^ [] = 146 ^ []]], -(substitution_of_equivalents)], (134 ^ _109216) ^ [] : [substitution_of_equivalents, 137 ^ _109216 : [(138 ^ _109216) ^ [_113894, _113896] : [is_a_theorem(equiv(_113896, _113894)), -(_113896 = _113894)]]], (154 ^ _109216) ^ [] : [modus_tollens, 157 ^ _109216 : [(158 ^ _109216) ^ [_114441, _114443] : [-(is_a_theorem(implies(implies(not _114441, not _114443), implies(_114443, _114441))))]]], (160 ^ _109216) ^ [] : [is_a_theorem(implies(implies(not 162 ^ [], not 161 ^ []), implies(161 ^ [], 162 ^ []))), -(modus_tollens)], (168 ^ _109216) ^ [] : [implies_1, 171 ^ _109216 : [(172 ^ _109216) ^ [_114845, _114847] : [-(is_a_theorem(implies(_114847, implies(_114845, _114847))))]]], (174 ^ _109216) ^ [] : [is_a_theorem(implies(175 ^ [], implies(176 ^ [], 175 ^ []))), -(implies_1)], (182 ^ _109216) ^ [] : [implies_2, 185 ^ _109216 : [(186 ^ _109216) ^ [_115230, _115232] : [-(is_a_theorem(implies(implies(_115232, implies(_115232, _115230)), implies(_115232, _115230))))]]], (188 ^ _109216) ^ [] : [is_a_theorem(implies(implies(189 ^ [], implies(189 ^ [], 190 ^ [])), implies(189 ^ [], 190 ^ []))), -(implies_2)], (196 ^ _109216) ^ [] : [implies_3, 199 ^ _109216 : [(200 ^ _109216) ^ [_115647, _115649, _115651] : [-(is_a_theorem(implies(implies(_115651, _115649), implies(implies(_115649, _115647), implies(_115651, _115647)))))]]], (202 ^ _109216) ^ [] : [is_a_theorem(implies(implies(203 ^ [], 204 ^ []), implies(implies(204 ^ [], 205 ^ []), implies(203 ^ [], 205 ^ [])))), -(implies_3)], (211 ^ _109216) ^ [] : [and_1, 214 ^ _109216 : [(215 ^ _109216) ^ [_116119, _116121] : [-(is_a_theorem(implies(and(_116121, _116119), _116121)))]]], (217 ^ _109216) ^ [] : [is_a_theorem(implies(and(218 ^ [], 219 ^ []), 218 ^ [])), -(and_1)], (225 ^ _109216) ^ [] : [and_2, 228 ^ _109216 : [(229 ^ _109216) ^ [_116504, _116506] : [-(is_a_theorem(implies(and(_116506, _116504), _116504)))]]], (231 ^ _109216) ^ [] : [is_a_theorem(implies(and(232 ^ [], 233 ^ []), 233 ^ [])), -(and_2)], (239 ^ _109216) ^ [] : [and_3, 242 ^ _109216 : [(243 ^ _109216) ^ [_116889, _116891] : [-(is_a_theorem(implies(_116891, implies(_116889, and(_116891, _116889)))))]]], (245 ^ _109216) ^ [] : [is_a_theorem(implies(246 ^ [], implies(247 ^ [], and(246 ^ [], 247 ^ [])))), -(and_3)], (253 ^ _109216) ^ [] : [or_1, 256 ^ _109216 : [(257 ^ _109216) ^ [_117283, _117285] : [-(is_a_theorem(implies(_117285, or(_117285, _117283))))]]], (259 ^ _109216) ^ [] : [is_a_theorem(implies(260 ^ [], or(260 ^ [], 261 ^ []))), -(or_1)], (267 ^ _109216) ^ [] : [or_2, 270 ^ _109216 : [(271 ^ _109216) ^ [_117668, _117670] : [-(is_a_theorem(implies(_117668, or(_117670, _117668))))]]], (273 ^ _109216) ^ [] : [is_a_theorem(implies(275 ^ [], or(274 ^ [], 275 ^ []))), -(or_2)], (281 ^ _109216) ^ [] : [or_3, 284 ^ _109216 : [(285 ^ _109216) ^ [_118067, _118069, _118071] : [-(is_a_theorem(implies(implies(_118071, _118067), implies(implies(_118069, _118067), implies(or(_118071, _118069), _118067)))))]]], (287 ^ _109216) ^ [] : [is_a_theorem(implies(implies(288 ^ [], 290 ^ []), implies(implies(289 ^ [], 290 ^ []), implies(or(288 ^ [], 289 ^ []), 290 ^ [])))), -(or_3)], (296 ^ _109216) ^ [] : [equivalence_1, 299 ^ _109216 : [(300 ^ _109216) ^ [_118551, _118553] : [-(is_a_theorem(implies(equiv(_118553, _118551), implies(_118553, _118551))))]]], (302 ^ _109216) ^ [] : [is_a_theorem(implies(equiv(303 ^ [], 304 ^ []), implies(303 ^ [], 304 ^ []))), -(equivalence_1)], (310 ^ _109216) ^ [] : [equivalence_2, 313 ^ _109216 : [(314 ^ _109216) ^ [_118945, _118947] : [-(is_a_theorem(implies(equiv(_118947, _118945), implies(_118945, _118947))))]]], (316 ^ _109216) ^ [] : [is_a_theorem(implies(equiv(317 ^ [], 318 ^ []), implies(318 ^ [], 317 ^ []))), -(equivalence_2)], (324 ^ _109216) ^ [] : [equivalence_3, 327 ^ _109216 : [(328 ^ _109216) ^ [_119339, _119341] : [-(is_a_theorem(implies(implies(_119341, _119339), implies(implies(_119339, _119341), equiv(_119341, _119339)))))]]], (330 ^ _109216) ^ [] : [is_a_theorem(implies(implies(331 ^ [], 332 ^ []), implies(implies(332 ^ [], 331 ^ []), equiv(331 ^ [], 332 ^ [])))), -(equivalence_3)], (338 ^ _109216) ^ [] : [kn1, 341 ^ _109216 : [(342 ^ _109216) ^ [_119737] : [-(is_a_theorem(implies(_119737, and(_119737, _119737))))]]], (344 ^ _109216) ^ [] : [is_a_theorem(implies(345 ^ [], and(345 ^ [], 345 ^ []))), -(kn1)], (351 ^ _109216) ^ [] : [kn2, 354 ^ _109216 : [(355 ^ _109216) ^ [_120073, _120075] : [-(is_a_theorem(implies(and(_120075, _120073), _120075)))]]], (357 ^ _109216) ^ [] : [is_a_theorem(implies(and(358 ^ [], 359 ^ []), 358 ^ [])), -(kn2)], (365 ^ _109216) ^ [] : [kn3, 368 ^ _109216 : [(369 ^ _109216) ^ [_120472, _120474, _120476] : [-(is_a_theorem(implies(implies(_120476, _120474), implies(not and(_120474, _120472), not and(_120472, _120476)))))]]], (371 ^ _109216) ^ [] : [is_a_theorem(implies(implies(372 ^ [], 373 ^ []), implies(not and(373 ^ [], 374 ^ []), not and(374 ^ [], 372 ^ [])))), -(kn3)], (380 ^ _109216) ^ [] : [cn1, 383 ^ _109216 : [(384 ^ _109216) ^ [_120974, _120976, _120978] : [-(is_a_theorem(implies(implies(_120978, _120976), implies(implies(_120976, _120974), implies(_120978, _120974)))))]]], (386 ^ _109216) ^ [] : [is_a_theorem(implies(implies(387 ^ [], 388 ^ []), implies(implies(388 ^ [], 389 ^ []), implies(387 ^ [], 389 ^ [])))), -(cn1)], (395 ^ _109216) ^ [] : [cn2, 398 ^ _109216 : [(399 ^ _109216) ^ [_121446, _121448] : [-(is_a_theorem(implies(_121448, implies(not _121448, _121446))))]]], (401 ^ _109216) ^ [] : [is_a_theorem(implies(402 ^ [], implies(not 402 ^ [], 403 ^ []))), -(cn2)], (409 ^ _109216) ^ [] : [cn3, 412 ^ _109216 : [(413 ^ _109216) ^ [_121821] : [-(is_a_theorem(implies(implies(not _121821, _121821), _121821)))]]], (415 ^ _109216) ^ [] : [is_a_theorem(implies(implies(not 416 ^ [], 416 ^ []), 416 ^ [])), -(cn3)], (422 ^ _109216) ^ [] : [r1, 425 ^ _109216 : [(426 ^ _109216) ^ [_122147] : [-(is_a_theorem(implies(or(_122147, _122147), _122147)))]]], (428 ^ _109216) ^ [] : [is_a_theorem(implies(or(429 ^ [], 429 ^ []), 429 ^ [])), -(r1)], (435 ^ _109216) ^ [] : [r2, 438 ^ _109216 : [(439 ^ _109216) ^ [_122483, _122485] : [-(is_a_theorem(implies(_122483, or(_122485, _122483))))]]], (441 ^ _109216) ^ [] : [is_a_theorem(implies(443 ^ [], or(442 ^ [], 443 ^ []))), -(r2)], (449 ^ _109216) ^ [] : [r3, 452 ^ _109216 : [(453 ^ _109216) ^ [_122868, _122870] : [-(is_a_theorem(implies(or(_122870, _122868), or(_122868, _122870))))]]], (455 ^ _109216) ^ [] : [is_a_theorem(implies(or(456 ^ [], 457 ^ []), or(457 ^ [], 456 ^ []))), -(r3)], (463 ^ _109216) ^ [] : [r4, 466 ^ _109216 : [(467 ^ _109216) ^ [_123276, _123278, _123280] : [-(is_a_theorem(implies(or(_123280, or(_123278, _123276)), or(_123278, or(_123280, _123276)))))]]], (469 ^ _109216) ^ [] : [is_a_theorem(implies(or(470 ^ [], or(471 ^ [], 472 ^ [])), or(471 ^ [], or(470 ^ [], 472 ^ [])))), -(r4)], (478 ^ _109216) ^ [] : [r5, 481 ^ _109216 : [(482 ^ _109216) ^ [_123745, _123747, _123749] : [-(is_a_theorem(implies(implies(_123747, _123745), implies(or(_123749, _123747), or(_123749, _123745)))))]]], (484 ^ _109216) ^ [] : [is_a_theorem(implies(implies(486 ^ [], 487 ^ []), implies(or(485 ^ [], 486 ^ []), or(485 ^ [], 487 ^ [])))), -(r5)], (493 ^ _109216) ^ [] : [op_or, 496 ^ _109216 : [(497 ^ _109216) ^ [_124380, _124382] : [-(or(_124382, _124380) = (not and(not _124382, not _124380)))]]], (499 ^ _109216) ^ [] : [op_and, 502 ^ _109216 : [(503 ^ _109216) ^ [_124553, _124555] : [-(and(_124555, _124553) = (not or(not _124555, not _124553)))]]], (505 ^ _109216) ^ [] : [op_implies_and, 508 ^ _109216 : [(509 ^ _109216) ^ [_124726, _124728] : [-(implies(_124728, _124726) = (not and(_124728, not _124726)))]]], (511 ^ _109216) ^ [] : [op_implies_or, 514 ^ _109216 : [(515 ^ _109216) ^ [_124897, _124899] : [-(implies(_124899, _124897) = or(not _124899, _124897))]]], (517 ^ _109216) ^ [] : [op_equiv, 520 ^ _109216 : [(521 ^ _109216) ^ [_125046, _125048] : [-(equiv(_125048, _125046) = and(implies(_125048, _125046), implies(_125046, _125048)))]]], (523 ^ _109216) ^ [] : [-(op_or)], (525 ^ _109216) ^ [] : [-(op_implies_and)], (527 ^ _109216) ^ [] : [-(op_equiv)], (529 ^ _109216) ^ [] : [-(modus_ponens)], (531 ^ _109216) ^ [] : [-(modus_tollens)], (533 ^ _109216) ^ [] : [-(implies_1)], (535 ^ _109216) ^ [] : [-(implies_2)], (537 ^ _109216) ^ [] : [-(implies_3)], (539 ^ _109216) ^ [] : [-(and_1)], (541 ^ _109216) ^ [] : [-(and_2)], (543 ^ _109216) ^ [] : [-(and_3)], (545 ^ _109216) ^ [] : [-(or_1)], (547 ^ _109216) ^ [] : [-(or_2)], (549 ^ _109216) ^ [] : [-(or_3)], (551 ^ _109216) ^ [] : [-(equivalence_1)], (553 ^ _109216) ^ [] : [-(equivalence_2)], (555 ^ _109216) ^ [] : [-(equivalence_3)], (557 ^ _109216) ^ [] : [-(substitution_of_equivalents)], (934 ^ _109216) ^ [] : [-(op_possibly)], (936 ^ _109216) ^ [] : [-(necessitation)], (938 ^ _109216) ^ [] : [-(axiom_K)], (940 ^ _109216) ^ [] : [-(axiom_M)], (942 ^ _109216) ^ [] : [-(axiom_4)], (944 ^ _109216) ^ [] : [-(axiom_B)], (946 ^ _109216) ^ [] : [-(op_possibly)], (948 ^ _109216) ^ [] : [-(op_or)], (950 ^ _109216) ^ [] : [-(op_implies)], (952 ^ _109216) ^ [] : [-(op_strict_implies)], (954 ^ _109216) ^ [] : [-(op_equiv)], (956 ^ _109216) ^ [] : [-(op_strict_equiv)], (910 ^ _109216) ^ [] : [op_possibly, 913 ^ _109216 : [(914 ^ _109216) ^ [_136051] : [-(possibly(_136051) = (not necessarily(not _136051)))]]], (916 ^ _109216) ^ [] : [op_necessarily, 919 ^ _109216 : [(920 ^ _109216) ^ [_136204] : [-(necessarily(_136204) = (not possibly(not _136204)))]]], (922 ^ _109216) ^ [] : [op_strict_implies, 925 ^ _109216 : [(926 ^ _109216) ^ [_136371, _136373] : [-(strict_implies(_136373, _136371) = necessarily(implies(_136373, _136371)))]]], (928 ^ _109216) ^ [] : [op_strict_equiv, 931 ^ _109216 : [(932 ^ _109216) ^ [_136520, _136522] : [-(strict_equiv(_136522, _136520) = and(strict_implies(_136522, _136520), strict_implies(_136520, _136522)))]]], (569 ^ _109216) ^ [] : [571 ^ _109216 : [(572 ^ _109216) ^ [] : [-(is_a_theorem(570 ^ []))], (574 ^ _109216) ^ [] : [is_a_theorem(necessarily(570 ^ []))]], -(necessitation)], (559 ^ _109216) ^ [] : [necessitation, 562 ^ _109216 : [(563 ^ _109216) ^ [_126265] : [is_a_theorem(_126265), -(is_a_theorem(necessarily(_126265)))]]], (592 ^ _109216) ^ [] : [595 ^ _109216 : [(596 ^ _109216) ^ [] : [-(is_a_theorem(593 ^ []))], (598 ^ _109216) ^ [] : [-(is_a_theorem(strict_implies(593 ^ [], 594 ^ [])))], (600 ^ _109216) ^ [] : [is_a_theorem(594 ^ [])]], -(modus_ponens_strict_implies)], (578 ^ _109216) ^ [] : [modus_ponens_strict_implies, 581 ^ _109216 : [(582 ^ _109216) ^ [_126765, _126767] : [-(is_a_theorem(_126765)), is_a_theorem(_126767), is_a_theorem(strict_implies(_126767, _126765))]]], (618 ^ _109216) ^ [] : [621 ^ _109216 : [(622 ^ _109216) ^ [] : [-(is_a_theorem(619 ^ []))], (624 ^ _109216) ^ [] : [-(is_a_theorem(620 ^ []))], (626 ^ _109216) ^ [] : [is_a_theorem(and(619 ^ [], 620 ^ []))]], -(adjunction)], (604 ^ _109216) ^ [] : [adjunction, 607 ^ _109216 : [(608 ^ _109216) ^ [_127475, _127477] : [-(is_a_theorem(and(_127477, _127475))), is_a_theorem(_127477), is_a_theorem(_127475)]]], (640 ^ _109216) ^ [] : [643 ^ _109216 : [(644 ^ _109216) ^ [] : [-(is_a_theorem(strict_equiv(641 ^ [], 642 ^ [])))], (646 ^ _109216) ^ [] : [641 ^ [] = 642 ^ []]], -(substitution_strict_equiv)], (630 ^ _109216) ^ [] : [substitution_strict_equiv, 633 ^ _109216 : [(634 ^ _109216) ^ [_128185, _128187] : [is_a_theorem(strict_equiv(_128187, _128185)), -(_128187 = _128185)]]], (650 ^ _109216) ^ [] : [axiom_K, 653 ^ _109216 : [(654 ^ _109216) ^ [_128732, _128734] : [-(is_a_theorem(implies(necessarily(implies(_128734, _128732)), implies(necessarily(_128734), necessarily(_128732)))))]]], (656 ^ _109216) ^ [] : [is_a_theorem(implies(necessarily(implies(657 ^ [], 658 ^ [])), implies(necessarily(657 ^ []), necessarily(658 ^ [])))), -(axiom_K)], (664 ^ _109216) ^ [] : [axiom_M, 667 ^ _109216 : [(668 ^ _109216) ^ [_129128] : [-(is_a_theorem(implies(necessarily(_129128), _129128)))]]], (670 ^ _109216) ^ [] : [is_a_theorem(implies(necessarily(671 ^ []), 671 ^ [])), -(axiom_M)], (677 ^ _109216) ^ [] : [axiom_4, 680 ^ _109216 : [(681 ^ _109216) ^ [_129448] : [-(is_a_theorem(implies(necessarily(_129448), necessarily(necessarily(_129448)))))]]], (683 ^ _109216) ^ [] : [is_a_theorem(implies(necessarily(684 ^ []), necessarily(necessarily(684 ^ [])))), -(axiom_4)], (690 ^ _109216) ^ [] : [axiom_B, 693 ^ _109216 : [(694 ^ _109216) ^ [_129776] : [-(is_a_theorem(implies(_129776, necessarily(possibly(_129776)))))]]], (696 ^ _109216) ^ [] : [is_a_theorem(implies(697 ^ [], necessarily(possibly(697 ^ [])))), -(axiom_B)], (703 ^ _109216) ^ [] : [axiom_5, 706 ^ _109216 : [(707 ^ _109216) ^ [_130100] : [-(is_a_theorem(implies(possibly(_130100), necessarily(possibly(_130100)))))]]], (709 ^ _109216) ^ [] : [is_a_theorem(implies(possibly(710 ^ []), necessarily(possibly(710 ^ [])))), -(axiom_5)], (716 ^ _109216) ^ [] : [axiom_s1, 719 ^ _109216 : [(720 ^ _109216) ^ [_130456, _130458, _130460] : [-(is_a_theorem(implies(and(necessarily(implies(_130460, _130458)), necessarily(implies(_130458, _130456))), necessarily(implies(_130460, _130456)))))]]], (722 ^ _109216) ^ [] : [is_a_theorem(implies(and(necessarily(implies(723 ^ [], 724 ^ [])), necessarily(implies(724 ^ [], 725 ^ []))), necessarily(implies(723 ^ [], 725 ^ [])))), -(axiom_s1)], (731 ^ _109216) ^ [] : [axiom_s2, 734 ^ _109216 : [(735 ^ _109216) ^ [_130950, _130952] : [-(is_a_theorem(strict_implies(possibly(and(_130952, _130950)), and(possibly(_130952), possibly(_130950)))))]]], (737 ^ _109216) ^ [] : [is_a_theorem(strict_implies(possibly(and(738 ^ [], 739 ^ [])), and(possibly(738 ^ []), possibly(739 ^ [])))), -(axiom_s2)], (745 ^ _109216) ^ [] : [axiom_s3, 748 ^ _109216 : [(749 ^ _109216) ^ [_131360, _131362] : [-(is_a_theorem(strict_implies(strict_implies(_131362, _131360), strict_implies(not possibly(_131360), not possibly(_131362)))))]]], (751 ^ _109216) ^ [] : [is_a_theorem(strict_implies(strict_implies(752 ^ [], 753 ^ []), strict_implies(not possibly(753 ^ []), not possibly(752 ^ [])))), -(axiom_s3)], (759 ^ _109216) ^ [] : [axiom_s4, 762 ^ _109216 : [(763 ^ _109216) ^ [_131760] : [-(is_a_theorem(strict_implies(necessarily(_131760), necessarily(necessarily(_131760)))))]]], (765 ^ _109216) ^ [] : [is_a_theorem(strict_implies(necessarily(766 ^ []), necessarily(necessarily(766 ^ [])))), -(axiom_s4)], (772 ^ _109216) ^ [] : [axiom_m1, 775 ^ _109216 : [(776 ^ _109216) ^ [_132102, _132104] : [-(is_a_theorem(strict_implies(and(_132104, _132102), and(_132102, _132104))))]]], (778 ^ _109216) ^ [] : [is_a_theorem(strict_implies(and(779 ^ [], 780 ^ []), and(780 ^ [], 779 ^ []))), -(axiom_m1)], (786 ^ _109216) ^ [] : [axiom_m2, 789 ^ _109216 : [(790 ^ _109216) ^ [_132496, _132498] : [-(is_a_theorem(strict_implies(and(_132498, _132496), _132498)))]]], (792 ^ _109216) ^ [] : [is_a_theorem(strict_implies(and(793 ^ [], 794 ^ []), 793 ^ [])), -(axiom_m2)], (800 ^ _109216) ^ [] : [axiom_m3, 803 ^ _109216 : [(804 ^ _109216) ^ [_132895, _132897, _132899] : [-(is_a_theorem(strict_implies(and(and(_132899, _132897), _132895), and(_132899, and(_132897, _132895)))))]]], (806 ^ _109216) ^ [] : [is_a_theorem(strict_implies(and(and(807 ^ [], 808 ^ []), 809 ^ []), and(807 ^ [], and(808 ^ [], 809 ^ [])))), -(axiom_m3)], (815 ^ _109216) ^ [] : [axiom_m4, 818 ^ _109216 : [(819 ^ _109216) ^ [_133353] : [-(is_a_theorem(strict_implies(_133353, and(_133353, _133353))))]]], (821 ^ _109216) ^ [] : [is_a_theorem(strict_implies(822 ^ [], and(822 ^ [], 822 ^ []))), -(axiom_m4)], (828 ^ _109216) ^ [] : [axiom_m5, 831 ^ _109216 : [(832 ^ _109216) ^ [_133703, _133705, _133707] : [-(is_a_theorem(strict_implies(and(strict_implies(_133707, _133705), strict_implies(_133705, _133703)), strict_implies(_133707, _133703))))]]], (834 ^ _109216) ^ [] : [is_a_theorem(strict_implies(and(strict_implies(835 ^ [], 836 ^ []), strict_implies(836 ^ [], 837 ^ [])), strict_implies(835 ^ [], 837 ^ []))), -(axiom_m5)], (843 ^ _109216) ^ [] : [axiom_m6, 846 ^ _109216 : [(847 ^ _109216) ^ [_134161] : [-(is_a_theorem(strict_implies(_134161, possibly(_134161))))]]], (849 ^ _109216) ^ [] : [is_a_theorem(strict_implies(850 ^ [], possibly(850 ^ []))), -(axiom_m6)], (856 ^ _109216) ^ [] : [axiom_m7, 859 ^ _109216 : [(860 ^ _109216) ^ [_134495, _134497] : [-(is_a_theorem(strict_implies(possibly(and(_134497, _134495)), _134497)))]]], (862 ^ _109216) ^ [] : [is_a_theorem(strict_implies(possibly(and(863 ^ [], 864 ^ [])), 863 ^ [])), -(axiom_m7)], (870 ^ _109216) ^ [] : [axiom_m8, 873 ^ _109216 : [(874 ^ _109216) ^ [_134886, _134888] : [-(is_a_theorem(strict_implies(strict_implies(_134888, _134886), strict_implies(possibly(_134888), possibly(_134886)))))]]], (876 ^ _109216) ^ [] : [is_a_theorem(strict_implies(strict_implies(877 ^ [], 878 ^ []), strict_implies(possibly(877 ^ []), possibly(878 ^ [])))), -(axiom_m8)], (884 ^ _109216) ^ [] : [axiom_m9, 887 ^ _109216 : [(888 ^ _109216) ^ [_135276] : [-(is_a_theorem(strict_implies(possibly(possibly(_135276)), possibly(_135276))))]]], (890 ^ _109216) ^ [] : [is_a_theorem(strict_implies(possibly(possibly(891 ^ [])), possibly(891 ^ []))), -(axiom_m9)], (897 ^ _109216) ^ [] : [axiom_m10, 900 ^ _109216 : [(901 ^ _109216) ^ [_135584] : [-(is_a_theorem(strict_implies(possibly(_135584), necessarily(possibly(_135584)))))]]], (903 ^ _109216) ^ [] : [is_a_theorem(strict_implies(possibly(904 ^ []), necessarily(possibly(904 ^ [])))), -(axiom_m10)]], input).
% 25.19/25.26  ncf('1',plain,[modus_ponens_strict_implies],start(958 ^ 0)).
% 25.19/25.26  ncf('1.1',plain,[-(modus_ponens_strict_implies), 598 : -(is_a_theorem(strict_implies(593 ^ [], 594 ^ [])))],extension(592 ^ 1)).
% 25.19/25.26  ncf('1.1.1',plain,[is_a_theorem(strict_implies(593 ^ [], 594 ^ [])), -(is_a_theorem(necessarily(implies(593 ^ [], 594 ^ [])))), strict_implies(593 ^ [], 594 ^ []) = necessarily(implies(593 ^ [], 594 ^ []))],extension(20 ^ 4,bind([[_109964, _109966], [necessarily(implies(593 ^ [], 594 ^ [])), strict_implies(593 ^ [], 594 ^ [])]]))).
% 25.19/25.26  ncf('1.1.1.1',plain,[is_a_theorem(necessarily(implies(593 ^ [], 594 ^ []))), 112 : -(is_a_theorem(implies(593 ^ [], 594 ^ []))), 112 : is_a_theorem(implies(necessarily(implies(593 ^ [], 594 ^ [])), implies(593 ^ [], 594 ^ []))), 112 : modus_ponens],extension(108 ^ 5,bind([[_113184, _113186], [implies(593 ^ [], 594 ^ []), necessarily(implies(593 ^ [], 594 ^ []))]]))).
% 25.19/25.26  ncf('1.1.1.1.1',plain,[is_a_theorem(implies(593 ^ [], 594 ^ [])), -(is_a_theorem(594 ^ [])), is_a_theorem(593 ^ [])],extension(112 ^ 8,bind([[_113184, _113186], [594 ^ [], 593 ^ []]]))).
% 25.19/25.26  ncf('1.1.1.1.1.1',plain,[is_a_theorem(594 ^ [])],extension(600 ^ 9)).
% 25.19/25.26  ncf('1.1.1.1.1.2',plain,[-(is_a_theorem(593 ^ []))],extension(596 ^ 9)).
% 25.19/25.26  ncf('1.1.1.1.2',plain,[-(is_a_theorem(implies(necessarily(implies(593 ^ [], 594 ^ [])), implies(593 ^ [], 594 ^ [])))), axiom_M],extension(664 ^ 8,bind([[_129128], [implies(593 ^ [], 594 ^ [])]]))).
% 25.19/25.26  ncf('1.1.1.1.2.1',plain,[-(axiom_M)],extension(940 ^ 9)).
% 25.19/25.26  ncf('1.1.1.1.3',plain,[-(modus_ponens)],extension(529 ^ 6)).
% 25.19/25.26  ncf('1.1.1.2',plain,[-(strict_implies(593 ^ [], 594 ^ []) = necessarily(implies(593 ^ [], 594 ^ []))), strict_implies(593 ^ [], 594 ^ []) = necessarily(implies(593 ^ [], 594 ^ [])), necessarily(implies(593 ^ [], 594 ^ [])) = necessarily(implies(593 ^ [], 594 ^ []))],extension(10 ^ 5,bind([[_109671, _109673, _109675], [necessarily(implies(593 ^ [], 594 ^ [])), necessarily(implies(593 ^ [], 594 ^ [])), strict_implies(593 ^ [], 594 ^ [])]]))).
% 25.19/25.26  ncf('1.1.1.2.1',plain,[-(strict_implies(593 ^ [], 594 ^ []) = necessarily(implies(593 ^ [], 594 ^ []))), op_strict_implies],extension(922 ^ 6,bind([[_136371, _136373], [594 ^ [], 593 ^ []]]))).
% 25.19/25.26  ncf('1.1.1.2.1.1',plain,[-(op_strict_implies)],extension(952 ^ 7)).
% 25.19/25.26  ncf('1.1.1.2.2',plain,[-(necessarily(implies(593 ^ [], 594 ^ [])) = necessarily(implies(593 ^ [], 594 ^ [])))],extension(2 ^ 6,bind([[_109360], [necessarily(implies(593 ^ [], 594 ^ []))]]))).
% 25.19/25.26  %-----------------------------------------------------
% 25.19/25.26  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------