TSTP Solution File: LCL549+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL549+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 : 600s
% DateTime : Sun Jul 17 14:37:38 EDT 2022
% Result : Theorem 9.93s 10.11s
% Output : Refutation 11.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 47
% Syntax : Number of clauses : 170 ( 119 unt; 1 nHn; 170 RR)
% Number of literals : 227 ( 0 equ; 63 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 25 ( 24 usr; 23 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
op_strict_implies,
file('LCL549+1.p',unknown),
[] ).
cnf(6,axiom,
op_strict_equiv,
file('LCL549+1.p',unknown),
[] ).
cnf(8,axiom,
op_implies_and,
file('LCL549+1.p',unknown),
[] ).
cnf(9,axiom,
op_equiv,
file('LCL549+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL549+1.p',unknown),
[] ).
cnf(12,axiom,
implies_1,
file('LCL549+1.p',unknown),
[] ).
cnf(13,axiom,
implies_2,
file('LCL549+1.p',unknown),
[] ).
cnf(14,axiom,
implies_3,
file('LCL549+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL549+1.p',unknown),
[] ).
cnf(16,axiom,
and_2,
file('LCL549+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL549+1.p',unknown),
[] ).
cnf(23,axiom,
equivalence_3,
file('LCL549+1.p',unknown),
[] ).
cnf(24,axiom,
substitution_of_equivalents,
file('LCL549+1.p',unknown),
[] ).
cnf(25,axiom,
op_possibly,
file('LCL549+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL549+1.p',unknown),
[] ).
cnf(27,axiom,
axiom_K,
file('LCL549+1.p',unknown),
[] ).
cnf(28,axiom,
axiom_M,
file('LCL549+1.p',unknown),
[] ).
cnf(29,axiom,
axiom_4,
file('LCL549+1.p',unknown),
[] ).
cnf(30,axiom,
axiom_B,
file('LCL549+1.p',unknown),
[] ).
cnf(31,axiom,
~ axiom_m10,
file('LCL549+1.p',unknown),
[] ).
cnf(32,axiom,
is_a_theorem(skc95),
file('LCL549+1.p',unknown),
[] ).
cnf(38,axiom,
is_a_theorem(implies__dfg(skc95,skc94)),
file('LCL549+1.p',unknown),
[] ).
cnf(44,axiom,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(skc155,skc154)) ),
file('LCL549+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ equal(skc155,skc154)
| substitution_strict_equiv ),
file('LCL549+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL549+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ implies_1
| is_a_theorem(implies__dfg(u,implies__dfg(v,u))) ),
file('LCL549+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL549+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL549+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL549+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ axiom_B
| is_a_theorem(implies__dfg(u,necessarily(possibly(u)))) ),
file('LCL549+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ axiom_4
| is_a_theorem(implies__dfg(necessarily(u),necessarily(necessarily(u)))) ),
file('LCL549+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ axiom_5
| is_a_theorem(implies__dfg(possibly(u),necessarily(possibly(u)))) ),
file('LCL549+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ is_a_theorem(implies__dfg(possibly(skc161),necessarily(possibly(skc161))))
| axiom_5 ),
file('LCL549+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ is_a_theorem(strict_implies(possibly(skc187),necessarily(possibly(skc187))))
| axiom_m10 ),
file('LCL549+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ op_possibly
| equal(not__dfg(necessarily(not__dfg(u))),possibly(u)) ),
file('LCL549+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL549+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL549+1.p',unknown),
[] ).
cnf(104,axiom,
( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
file('LCL549+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL549+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL549+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL549+1.p',unknown),
[] ).
cnf(112,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL549+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL549+1.p',unknown),
[] ).
cnf(121,axiom,
( ~ axiom_K
| is_a_theorem(implies__dfg(necessarily(implies__dfg(u,v)),implies__dfg(necessarily(u),necessarily(v)))) ),
file('LCL549+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ op_strict_equiv
| equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)) ),
file('LCL549+1.p',unknown),
[] ).
cnf(126,axiom,
( ~ implies_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))) ),
file('LCL549+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
file('LCL549+1.p',unknown),
[] ).
cnf(148,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[47,28]),
[iquote('0:MRR:47.0,28.0')] ).
cnf(149,plain,
is_a_theorem(implies__dfg(u,necessarily(possibly(u)))),
inference(mrr,[status(thm)],[70,30]),
[iquote('0:MRR:70.0,30.0')] ).
cnf(150,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(u)) ),
inference(mrr,[status(thm)],[69,26]),
[iquote('0:MRR:69.1,26.0')] ).
cnf(154,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(mrr,[status(thm)],[55,16]),
[iquote('0:MRR:55.0,16.0')] ).
cnf(155,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[53,15]),
[iquote('0:MRR:53.0,15.0')] ).
cnf(157,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(mrr,[status(thm)],[51,12]),
[iquote('0:MRR:51.0,12.0')] ).
cnf(158,plain,
equal(not__dfg(necessarily(not__dfg(u))),possibly(u)),
inference(mrr,[status(thm)],[92,25]),
[iquote('0:MRR:92.0,25.0')] ).
cnf(159,plain,
~ is_a_theorem(strict_implies(possibly(skc187),necessarily(possibly(skc187)))),
inference(mrr,[status(thm)],[91,31]),
[iquote('0:MRR:91.1,31.0')] ).
cnf(160,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(necessarily(u)))),
inference(mrr,[status(thm)],[80,29]),
[iquote('0:MRR:80.0,29.0')] ).
cnf(161,plain,
equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
inference(mrr,[status(thm)],[107,4]),
[iquote('0:MRR:107.0,4.0')] ).
cnf(164,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[95,17]),
[iquote('0:MRR:95.0,17.0')] ).
cnf(165,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[94,24]),
[iquote('0:MRR:94.0,24.0')] ).
cnf(166,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[108,8]),
[iquote('0:MRR:108.0,8.0')] ).
cnf(174,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[112,13]),
[iquote('0:MRR:112.0,13.0')] ).
cnf(177,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[109,10]),
[iquote('0:MRR:109.1,10.0')] ).
cnf(178,plain,
equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)),
inference(mrr,[status(thm)],[125,6]),
[iquote('0:MRR:125.0,6.0')] ).
cnf(179,plain,
( ~ axiom_K
| is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(necessarily(u),necessarily(v)))) ),
inference(rew,[status(thm),theory(equality)],[161,121]),
[iquote('0:Rew:161.0,121.1')] ).
cnf(180,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(necessarily(u),necessarily(v)))),
inference(mrr,[status(thm)],[179,27]),
[iquote('0:MRR:179.0,27.0')] ).
cnf(181,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[120,9]),
[iquote('0:MRR:120.0,9.0')] ).
cnf(182,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))),
inference(mrr,[status(thm)],[128,23]),
[iquote('0:MRR:128.0,23.0')] ).
cnf(183,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(mrr,[status(thm)],[126,14]),
[iquote('0:MRR:126.0,14.0')] ).
cnf(192,plain,
substitution_strict_equiv,
inference(spt,[spt(split,[position(s1)])],[44]),
[iquote('1:Spt:44.0')] ).
cnf(193,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[104,192]),
[iquote('1:MRR:104.0,192.0')] ).
cnf(215,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[161,148]),
[iquote('0:SpR:161.0,148.0')] ).
cnf(216,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(spr,[status(thm),theory(equality)],[161,150]),
[iquote('0:SpR:161.0,150.1')] ).
cnf(263,plain,
equal(not__dfg(necessarily(implies__dfg(u,v))),possibly(and__dfg(u,not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[166,158]),
[iquote('0:SpR:166.0,158.0')] ).
cnf(275,plain,
equal(possibly(and__dfg(u,not__dfg(v))),not__dfg(strict_implies(u,v))),
inference(rew,[status(thm),theory(equality)],[161,263]),
[iquote('0:Rew:161.0,263.0')] ).
cnf(287,plain,
( ~ axiom_5
| is_a_theorem(strict_implies(possibly(u),necessarily(possibly(u)))) ),
inference(sor,[status(thm)],[216,82]),
[iquote('0:SoR:216.0,82.1')] ).
cnf(295,plain,
is_a_theorem(strict_implies(and__dfg(u,v),v)),
inference(sor,[status(thm)],[216,154]),
[iquote('0:SoR:216.0,154.0')] ).
cnf(298,plain,
is_a_theorem(strict_implies(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[216,157]),
[iquote('0:SoR:216.0,157.0')] ).
cnf(304,plain,
is_a_theorem(strict_implies(skc95,skc94)),
inference(sor,[status(thm)],[216,38]),
[iquote('0:SoR:216.0,38.0')] ).
cnf(348,plain,
~ axiom_5,
inference(res,[status(thm),theory(equality)],[287,159]),
[iquote('0:Res:287.1,159.0')] ).
cnf(349,plain,
~ is_a_theorem(implies__dfg(possibly(skc161),necessarily(possibly(skc161)))),
inference(mrr,[status(thm)],[83,348]),
[iquote('0:MRR:83.1,348.0')] ).
cnf(422,plain,
( ~ is_a_theorem(skc95)
| is_a_theorem(skc94) ),
inference(res,[status(thm),theory(equality)],[38,177]),
[iquote('0:Res:38.0,177.1')] ).
cnf(429,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[157,177]),
[iquote('0:Res:157.0,177.1')] ).
cnf(439,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[215,177]),
[iquote('0:Res:215.0,177.1')] ).
cnf(440,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(necessarily(u),necessarily(v))) ),
inference(res,[status(thm),theory(equality)],[180,177]),
[iquote('0:Res:180.0,177.1')] ).
cnf(446,plain,
is_a_theorem(skc94),
inference(ssi,[status(thm)],[422,32]),
[iquote('0:SSi:422.0,32.0')] ).
cnf(453,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[174,177]),
[iquote('0:Res:174.0,177.1')] ).
cnf(467,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(v,u))),
inference(spr,[status(thm),theory(equality)],[178,154]),
[iquote('0:SpR:178.0,154.0')] ).
cnf(468,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(u,v))),
inference(spr,[status(thm),theory(equality)],[178,155]),
[iquote('0:SpR:178.0,155.0')] ).
cnf(602,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[467,177]),
[iquote('0:Res:467.0,177.1')] ).
cnf(604,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(res,[status(thm),theory(equality)],[468,177]),
[iquote('0:Res:468.0,177.1')] ).
cnf(608,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,u),equiv__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[182,177]),
[iquote('0:Res:182.0,177.1')] ).
cnf(621,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[183,177]),
[iquote('0:Res:183.0,177.1')] ).
cnf(2085,plain,
is_a_theorem(implies__dfg(necessarily(skc95),necessarily(skc94))),
inference(sor,[status(thm)],[440,304]),
[iquote('0:SoR:440.0,304.0')] ).
cnf(2089,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(implies__dfg(v,u)))),
inference(sor,[status(thm)],[440,298]),
[iquote('0:SoR:440.0,298.0')] ).
cnf(2102,plain,
is_a_theorem(implies__dfg(necessarily(u),strict_implies(v,u))),
inference(rew,[status(thm),theory(equality)],[161,2089]),
[iquote('0:Rew:161.0,2089.0')] ).
cnf(2127,plain,
( ~ is_a_theorem(necessarily(skc95))
| is_a_theorem(necessarily(skc94)) ),
inference(res,[status(thm),theory(equality)],[2085,177]),
[iquote('0:Res:2085.0,177.1')] ).
cnf(2128,plain,
is_a_theorem(necessarily(skc94)),
inference(ssi,[status(thm)],[2127,150,32]),
[iquote('0:SSi:2127.0,150.0,32.1')] ).
cnf(2136,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[2102,177]),
[iquote('0:Res:2102.0,177.1')] ).
cnf(2201,plain,
is_a_theorem(strict_implies(u,skc94)),
inference(sor,[status(thm)],[2136,2128]),
[iquote('0:SoR:2136.0,2128.0')] ).
cnf(2206,plain,
is_a_theorem(implies__dfg(u,skc94)),
inference(sor,[status(thm)],[439,2201]),
[iquote('0:SoR:439.0,2201.0')] ).
cnf(4238,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(u,skc94))),
inference(sor,[status(thm)],[608,2206]),
[iquote('0:SoR:608.0,2206.0')] ).
cnf(4250,plain,
is_a_theorem(implies__dfg(implies__dfg(necessarily(necessarily(u)),necessarily(u)),equiv__dfg(necessarily(u),necessarily(necessarily(u))))),
inference(sor,[status(thm)],[608,160]),
[iquote('0:SoR:608.0,160.0')] ).
cnf(4416,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(v,u))),
inference(sor,[status(thm)],[621,2206]),
[iquote('0:SoR:621.0,2206.0')] ).
cnf(5911,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[4238,177]),
[iquote('0:Res:4238.0,177.1')] ).
cnf(5921,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[453,4416]),
[iquote('0:SoR:453.0,4416.0')] ).
cnf(5929,plain,
is_a_theorem(strict_implies(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[216,5921]),
[iquote('0:SoR:216.0,5921.0')] ).
cnf(5930,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[5921,177]),
[iquote('0:Res:5921.0,177.1')] ).
cnf(5935,plain,
is_a_theorem(implies__dfg(necessarily(implies__dfg(skc94,u)),necessarily(u))),
inference(sor,[status(thm)],[440,5929]),
[iquote('0:SoR:440.0,5929.0')] ).
cnf(5938,plain,
is_a_theorem(implies__dfg(strict_implies(skc94,u),necessarily(u))),
inference(rew,[status(thm),theory(equality)],[161,5935]),
[iquote('0:Rew:161.0,5935.0')] ).
cnf(5972,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[5930,164]),
[iquote('0:SoR:5930.0,164.0')] ).
cnf(6012,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[216,5972]),
[iquote('0:SoR:216.0,5972.0')] ).
cnf(6064,plain,
( ~ is_a_theorem(strict_implies(skc94,u))
| is_a_theorem(necessarily(u)) ),
inference(res,[status(thm),theory(equality)],[5938,177]),
[iquote('0:Res:5938.0,177.1')] ).
cnf(6630,plain,
is_a_theorem(necessarily(and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[6064,6012]),
[iquote('0:SoR:6064.0,6012.0')] ).
cnf(6649,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[2136,6630]),
[iquote('0:SoR:2136.0,6630.0')] ).
cnf(6654,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[439,6649]),
[iquote('0:SoR:439.0,6649.0')] ).
cnf(11372,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(sor,[status(thm)],[5911,429]),
[iquote('0:SoR:5911.0,429.1')] ).
cnf(11395,plain,
is_a_theorem(equiv__dfg(and__dfg(skc94,skc94),skc94)),
inference(sor,[status(thm)],[5911,6654]),
[iquote('0:SoR:5911.0,6654.0')] ).
cnf(11429,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc94),skc94)),
inference(sor,[status(thm)],[5911,157]),
[iquote('0:SoR:5911.0,157.0')] ).
cnf(12966,plain,
equal(and__dfg(skc94,skc94),skc94),
inference(res,[status(thm),theory(equality)],[11395,165]),
[iquote('0:Res:11395.0,165.0')] ).
cnf(13309,plain,
equal(implies__dfg(u,skc94),skc94),
inference(res,[status(thm),theory(equality)],[11429,165]),
[iquote('0:Res:11429.0,165.0')] ).
cnf(13358,plain,
equal(and__dfg(skc94,implies__dfg(skc94,u)),equiv__dfg(u,skc94)),
inference(spr,[status(thm),theory(equality)],[13309,181]),
[iquote('0:SpR:13309.0,181.0')] ).
cnf(14529,plain,
( ~ is_a_theorem(u)
| equal(u,skc94) ),
inference(res,[status(thm),theory(equality)],[11372,165]),
[iquote('0:Res:11372.1,165.0')] ).
cnf(14671,plain,
equal(strict_implies(and__dfg(u,v),v),skc94),
inference(ems,[status(thm)],[14529,295]),
[iquote('0:EmS:14529.0,295.0')] ).
cnf(14674,plain,
equal(strict_implies(implies__dfg(skc94,u),u),skc94),
inference(ems,[status(thm)],[14529,5929]),
[iquote('0:EmS:14529.0,5929.0')] ).
cnf(14690,plain,
equal(strict_implies(u,and__dfg(skc94,u)),skc94),
inference(ems,[status(thm)],[14529,6012]),
[iquote('0:EmS:14529.0,6012.0')] ).
cnf(14694,plain,
equal(strict_implies(u,implies__dfg(v,u)),skc94),
inference(ems,[status(thm)],[14529,298]),
[iquote('0:EmS:14529.0,298.0')] ).
cnf(14836,plain,
equal(implies__dfg(u,necessarily(possibly(u))),skc94),
inference(ems,[status(thm)],[14529,149]),
[iquote('0:EmS:14529.0,149.0')] ).
cnf(14838,plain,
equal(implies__dfg(necessarily(u),u),skc94),
inference(ems,[status(thm)],[14529,148]),
[iquote('0:EmS:14529.0,148.0')] ).
cnf(14937,plain,
is_a_theorem(implies__dfg(skc94,equiv__dfg(necessarily(u),necessarily(necessarily(u))))),
inference(rew,[status(thm),theory(equality)],[14838,4250]),
[iquote('0:Rew:14838.0,4250.0')] ).
cnf(15625,plain,
is_a_theorem(equiv__dfg(necessarily(u),necessarily(necessarily(u)))),
inference(sor,[status(thm)],[5930,14937]),
[iquote('0:SoR:5930.0,14937.0')] ).
cnf(16441,plain,
equal(and__dfg(skc94,strict_implies(u,implies__dfg(skc94,u))),strict_equiv(implies__dfg(skc94,u),u)),
inference(spr,[status(thm),theory(equality)],[14674,178]),
[iquote('0:SpR:14674.0,178.0')] ).
cnf(16449,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[14694,16441]),
[iquote('0:Rew:14694.0,16441.0')] ).
cnf(16450,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),skc94),
inference(rew,[status(thm),theory(equality)],[12966,16449]),
[iquote('0:Rew:12966.0,16449.0')] ).
cnf(16454,plain,
equal(and__dfg(skc94,strict_implies(and__dfg(skc94,u),u)),strict_equiv(u,and__dfg(skc94,u))),
inference(spr,[status(thm),theory(equality)],[14690,178]),
[iquote('0:SpR:14690.0,178.0')] ).
cnf(16462,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[14671,16454]),
[iquote('0:Rew:14671.0,16454.0')] ).
cnf(16463,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[12966,16462]),
[iquote('0:Rew:12966.0,16462.0')] ).
cnf(16600,plain,
equal(necessarily(necessarily(u)),necessarily(u)),
inference(res,[status(thm),theory(equality)],[15625,165]),
[iquote('0:Res:15625.0,165.0')] ).
cnf(17680,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[16450,193]),
[iquote('1:SpL:16450.0,193.0')] ).
cnf(17682,plain,
equal(implies__dfg(skc94,u),u),
inference(mrr,[status(thm)],[17680,446]),
[iquote('1:MRR:17680.0,446.0')] ).
cnf(17799,plain,
equal(and__dfg(skc94,u),equiv__dfg(u,skc94)),
inference(rew,[status(thm),theory(equality)],[17682,13358]),
[iquote('1:Rew:17682.0,13358.0')] ).
cnf(17948,plain,
equal(strict_equiv(u,equiv__dfg(u,skc94)),skc94),
inference(rew,[status(thm),theory(equality)],[17799,16463]),
[iquote('1:Rew:17799.0,16463.0')] ).
cnf(18015,plain,
equal(strict_implies(skc94,u),necessarily(u)),
inference(spr,[status(thm),theory(equality)],[17682,161]),
[iquote('1:SpR:17682.0,161.0')] ).
cnf(18940,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),implies__dfg(skc94,u)),
inference(spr,[status(thm),theory(equality)],[17799,166]),
[iquote('1:SpR:17799.0,166.0')] ).
cnf(18941,plain,
equal(possibly(equiv__dfg(not__dfg(u),skc94)),not__dfg(strict_implies(skc94,u))),
inference(spr,[status(thm),theory(equality)],[17799,275]),
[iquote('1:SpR:17799.0,275.0')] ).
cnf(18951,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),u),
inference(rew,[status(thm),theory(equality)],[17682,18940]),
[iquote('1:Rew:17682.0,18940.0')] ).
cnf(18952,plain,
equal(possibly(equiv__dfg(not__dfg(u),skc94)),not__dfg(necessarily(u))),
inference(rew,[status(thm),theory(equality)],[18015,18941]),
[iquote('1:Rew:18015.0,18941.0')] ).
cnf(19006,plain,
( ~ is_a_theorem(skc94)
| equal(equiv__dfg(u,skc94),u) ),
inference(spl,[status(thm),theory(equality)],[17948,193]),
[iquote('1:SpL:17948.0,193.0')] ).
cnf(19007,plain,
equal(equiv__dfg(u,skc94),u),
inference(mrr,[status(thm)],[19006,446]),
[iquote('1:MRR:19006.0,446.0')] ).
cnf(19095,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[19007,18951]),
[iquote('1:Rew:19007.0,18951.0')] ).
cnf(19096,plain,
equal(not__dfg(necessarily(u)),possibly(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[19007,18952]),
[iquote('1:Rew:19007.0,18952.0')] ).
cnf(22955,plain,
equal(possibly(not__dfg(necessarily(u))),not__dfg(necessarily(u))),
inference(spr,[status(thm),theory(equality)],[16600,19096]),
[iquote('1:SpR:16600.0,19096.0')] ).
cnf(22959,plain,
equal(possibly(possibly(not__dfg(u))),possibly(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[19096,22955]),
[iquote('1:Rew:19096.0,22955.0')] ).
cnf(24785,plain,
equal(possibly(possibly(u)),possibly(u)),
inference(spr,[status(thm),theory(equality)],[19095,22959]),
[iquote('1:SpR:19095.0,22959.0')] ).
cnf(24864,plain,
equal(implies__dfg(possibly(u),necessarily(possibly(u))),skc94),
inference(spr,[status(thm),theory(equality)],[24785,14836]),
[iquote('1:SpR:24785.0,14836.0')] ).
cnf(24881,plain,
~ is_a_theorem(skc94),
inference(rew,[status(thm),theory(equality)],[24864,349]),
[iquote('1:Rew:24864.0,349.0')] ).
cnf(24882,plain,
$false,
inference(mrr,[status(thm)],[24881,446]),
[iquote('1:MRR:24881.0,446.0')] ).
cnf(24892,plain,
~ substitution_strict_equiv,
inference(spt,[spt(split,[position(sa)])],[24882,192]),
[iquote('1:Spt:24882.0,44.0,192.0')] ).
cnf(24893,plain,
is_a_theorem(strict_equiv(skc155,skc154)),
inference(spt,[spt(split,[position(s2)])],[44]),
[iquote('1:Spt:24882.0,44.1')] ).
cnf(24896,plain,
~ equal(skc155,skc154),
inference(mrr,[status(thm)],[45,24892]),
[iquote('1:MRR:45.1,24892.0')] ).
cnf(24909,plain,
is_a_theorem(strict_implies(skc155,skc154)),
inference(sor,[status(thm)],[604,24893]),
[iquote('1:SoR:604.0,24893.0')] ).
cnf(24910,plain,
is_a_theorem(strict_implies(skc154,skc155)),
inference(sor,[status(thm)],[602,24893]),
[iquote('1:SoR:602.0,24893.0')] ).
cnf(24919,plain,
is_a_theorem(implies__dfg(skc155,skc154)),
inference(sor,[status(thm)],[439,24909]),
[iquote('1:SoR:439.0,24909.0')] ).
cnf(24923,plain,
is_a_theorem(implies__dfg(skc154,skc155)),
inference(sor,[status(thm)],[439,24910]),
[iquote('1:SoR:439.0,24910.0')] ).
cnf(24925,plain,
equal(implies__dfg(skc155,skc154),skc94),
inference(ems,[status(thm)],[14529,24919]),
[iquote('1:EmS:14529.0,24919.0')] ).
cnf(24950,plain,
equal(implies__dfg(skc154,skc155),skc94),
inference(ems,[status(thm)],[14529,24923]),
[iquote('1:EmS:14529.0,24923.0')] ).
cnf(24977,plain,
equal(and__dfg(implies__dfg(skc154,skc155),skc94),equiv__dfg(skc154,skc155)),
inference(spr,[status(thm),theory(equality)],[24925,181]),
[iquote('1:SpR:24925.0,181.0')] ).
cnf(24985,plain,
equal(and__dfg(skc94,skc94),equiv__dfg(skc154,skc155)),
inference(rew,[status(thm),theory(equality)],[24950,24977]),
[iquote('1:Rew:24950.0,24977.0')] ).
cnf(24986,plain,
equal(equiv__dfg(skc154,skc155),skc94),
inference(rew,[status(thm),theory(equality)],[12966,24985]),
[iquote('1:Rew:12966.0,24985.0')] ).
cnf(25005,plain,
( ~ is_a_theorem(skc94)
| equal(skc155,skc154) ),
inference(spl,[status(thm),theory(equality)],[24986,165]),
[iquote('1:SpL:24986.0,165.0')] ).
cnf(25006,plain,
$false,
inference(mrr,[status(thm)],[25005,446,24896]),
[iquote('1:MRR:25005.0,25005.1,446.0,24896.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL549+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 17:34:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.93/10.11
% 9.93/10.11 SPASS V 3.9
% 9.93/10.11 SPASS beiseite: Proof found.
% 9.93/10.11 % SZS status Theorem
% 9.93/10.11 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.93/10.11 SPASS derived 16922 clauses, backtracked 2592 clauses, performed 3 splits and kept 10936 clauses.
% 9.93/10.11 SPASS allocated 127205 KBytes.
% 9.93/10.11 SPASS spent 0:00:09.74 on the problem.
% 9.93/10.11 0:00:00.04 for the input.
% 9.93/10.11 0:00:00.06 for the FLOTTER CNF translation.
% 9.93/10.11 0:00:00.18 for inferences.
% 9.93/10.11 0:00:00.24 for the backtracking.
% 9.93/10.11 0:00:09.10 for the reduction.
% 9.93/10.11
% 9.93/10.11
% 9.93/10.11 Here is a proof with depth 16, length 170 :
% 9.93/10.11 % SZS output start Refutation
% See solution above
% 11.07/11.26 Formulae used in the proof : s1_0_op_strict_implies s1_0_op_strict_equiv hilbert_op_implies_and hilbert_op_equiv hilbert_modus_ponens hilbert_implies_1 hilbert_implies_2 hilbert_implies_3 hilbert_and_1 hilbert_and_2 hilbert_and_3 hilbert_equivalence_3 substitution_of_equivalents km4b_op_possibly km4b_necessitation km4b_axiom_K km4b_axiom_M km4b_axiom_4 km4b_axiom_B s1_0_m10_axiom_m10 modus_ponens axiom_M and_3 substitution_strict_equiv implies_1 and_1 and_2 necessitation axiom_B axiom_4 axiom_5 axiom_m10 op_possibly op_strict_implies op_implies_and implies_2 op_equiv axiom_K op_strict_equiv implies_3 equivalence_3
% 11.07/11.26
%------------------------------------------------------------------------------