TSTP Solution File: LCL546+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL546+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 14:37:37 EDT 2022
% Result : Theorem 17.47s 17.71s
% Output : Refutation 19.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 55
% Syntax : Number of clauses : 291 ( 207 unt; 1 nHn; 291 RR)
% Number of literals : 383 ( 0 equ; 96 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 29 ( 28 usr; 27 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
op_strict_implies,
file('LCL546+1.p',unknown),
[] ).
cnf(6,axiom,
op_strict_equiv,
file('LCL546+1.p',unknown),
[] ).
cnf(7,axiom,
op_or,
file('LCL546+1.p',unknown),
[] ).
cnf(8,axiom,
op_implies_and,
file('LCL546+1.p',unknown),
[] ).
cnf(9,axiom,
op_equiv,
file('LCL546+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL546+1.p',unknown),
[] ).
cnf(11,axiom,
modus_tollens,
file('LCL546+1.p',unknown),
[] ).
cnf(12,axiom,
implies_1,
file('LCL546+1.p',unknown),
[] ).
cnf(13,axiom,
implies_2,
file('LCL546+1.p',unknown),
[] ).
cnf(14,axiom,
implies_3,
file('LCL546+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL546+1.p',unknown),
[] ).
cnf(16,axiom,
and_2,
file('LCL546+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL546+1.p',unknown),
[] ).
cnf(18,axiom,
or_1,
file('LCL546+1.p',unknown),
[] ).
cnf(23,axiom,
equivalence_3,
file('LCL546+1.p',unknown),
[] ).
cnf(24,axiom,
substitution_of_equivalents,
file('LCL546+1.p',unknown),
[] ).
cnf(25,axiom,
op_possibly,
file('LCL546+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL546+1.p',unknown),
[] ).
cnf(27,axiom,
axiom_K,
file('LCL546+1.p',unknown),
[] ).
cnf(28,axiom,
axiom_M,
file('LCL546+1.p',unknown),
[] ).
cnf(29,axiom,
axiom_4,
file('LCL546+1.p',unknown),
[] ).
cnf(30,axiom,
axiom_B,
file('LCL546+1.p',unknown),
[] ).
cnf(31,axiom,
~ axiom_m6,
file('LCL546+1.p',unknown),
[] ).
cnf(32,axiom,
is_a_theorem(skc95),
file('LCL546+1.p',unknown),
[] ).
cnf(38,axiom,
is_a_theorem(implies__dfg(skc95,skc94)),
file('LCL546+1.p',unknown),
[] ).
cnf(44,axiom,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(skc155,skc154)) ),
file('LCL546+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ equal(skc155,skc154)
| substitution_strict_equiv ),
file('LCL546+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL546+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ is_a_theorem(strict_implies(skc181,possibly(skc181)))
| axiom_m6 ),
file('LCL546+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ implies_1
| is_a_theorem(implies__dfg(u,implies__dfg(v,u))) ),
file('LCL546+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL546+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL546+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ or_1
| is_a_theorem(implies__dfg(u,or__dfg(u,v))) ),
file('LCL546+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL546+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ axiom_B
| is_a_theorem(implies__dfg(u,necessarily(possibly(u)))) ),
file('LCL546+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ axiom_4
| is_a_theorem(implies__dfg(necessarily(u),necessarily(necessarily(u)))) ),
file('LCL546+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ op_possibly
| equal(not__dfg(necessarily(not__dfg(u))),possibly(u)) ),
file('LCL546+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL546+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL546+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL546+1.p',unknown),
[] ).
cnf(102,axiom,
( ~ is_a_theorem(implies__dfg(or__dfg(skc142,skc141),or__dfg(skc141,skc142)))
| r3 ),
file('LCL546+1.p',unknown),
[] ).
cnf(104,axiom,
( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
file('LCL546+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL546+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL546+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL546+1.p',unknown),
[] ).
cnf(110,axiom,
( ~ modus_tollens
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))) ),
file('LCL546+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('LCL546+1.p',unknown),
[] ).
cnf(114,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL546+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL546+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('LCL546+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('LCL546+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('LCL546+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('LCL546+1.p',unknown),
[] ).
cnf(134,axiom,
( ~ r5
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))) ),
file('LCL546+1.p',unknown),
[] ).
cnf(135,axiom,
( ~ is_a_theorem(implies__dfg(implies__dfg(skc147,skc146),implies__dfg(or__dfg(skc148,skc147),or__dfg(skc148,skc146))))
| r5 ),
file('LCL546+1.p',unknown),
[] ).
cnf(148,plain,
~ is_a_theorem(strict_implies(skc181,possibly(skc181))),
inference(mrr,[status(thm)],[50,31]),
[iquote('0:MRR:50.1,31.0')] ).
cnf(149,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[47,28]),
[iquote('0:MRR:47.0,28.0')] ).
cnf(150,plain,
is_a_theorem(implies__dfg(u,necessarily(possibly(u)))),
inference(mrr,[status(thm)],[70,30]),
[iquote('0:MRR:70.0,30.0')] ).
cnf(151,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(u,or__dfg(u,v))),
inference(mrr,[status(thm)],[57,18]),
[iquote('0:MRR:57.0,18.0')] ).
cnf(155,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(156,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(158,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(159,plain,
equal(not__dfg(necessarily(not__dfg(u))),possibly(u)),
inference(mrr,[status(thm)],[92,25]),
[iquote('0:MRR:92.0,25.0')] ).
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(167,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[166,114]),
[iquote('0:Rew:166.0,114.1')] ).
cnf(168,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[167,7]),
[iquote('0:MRR:167.0,7.0')] ).
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(175,plain,
( ~ modus_tollens
| is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[168,110]),
[iquote('0:Rew:168.0,110.1')] ).
cnf(176,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(mrr,[status(thm)],[175,11]),
[iquote('0:MRR:175.0,11.0')] ).
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(194,plain,
equal(not__dfg(necessarily(possibly(u))),possibly(necessarily(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[159]),
[iquote('0:SpR:159.0,159.0')] ).
cnf(205,plain,
is_a_theorem(or__dfg(u,necessarily(possibly(not__dfg(u))))),
inference(spr,[status(thm),theory(equality)],[168,150]),
[iquote('0:SpR:168.0,150.0')] ).
cnf(218,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[161,149]),
[iquote('0:SpR:161.0,149.0')] ).
cnf(219,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(spr,[status(thm),theory(equality)],[161,151]),
[iquote('0:SpR:161.0,151.1')] ).
cnf(222,plain,
equal(necessarily(or__dfg(u,v)),strict_implies(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[168,161]),
[iquote('0:SpR:168.0,161.0')] ).
cnf(263,plain,
equal(not__dfg(necessarily(implies__dfg(u,v))),possibly(and__dfg(u,not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[166,159]),
[iquote('0:SpR:166.0,159.0')] ).
cnf(264,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),w),implies__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[166,168]),
[iquote('0:SpR:166.0,168.0')] ).
cnf(272,plain,
equal(not__dfg(and__dfg(u,possibly(v))),implies__dfg(u,necessarily(not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[159,166]),
[iquote('0:SpR:159.0,166.0')] ).
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(282,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(not__dfg(v))),or__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[168,176]),
[iquote('0:SpR:168.0,176.0')] ).
cnf(294,plain,
is_a_theorem(strict_implies(and__dfg(u,v),u)),
inference(sor,[status(thm)],[219,156]),
[iquote('0:SoR:219.0,156.0')] ).
cnf(295,plain,
is_a_theorem(strict_implies(and__dfg(u,v),v)),
inference(sor,[status(thm)],[219,155]),
[iquote('0:SoR:219.0,155.0')] ).
cnf(298,plain,
is_a_theorem(strict_implies(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[219,158]),
[iquote('0:SoR:219.0,158.0')] ).
cnf(299,plain,
is_a_theorem(strict_implies(u,or__dfg(u,v))),
inference(sor,[status(thm)],[219,154]),
[iquote('0:SoR:219.0,154.0')] ).
cnf(301,plain,
is_a_theorem(strict_implies(u,necessarily(possibly(u)))),
inference(sor,[status(thm)],[219,150]),
[iquote('0:SoR:219.0,150.0')] ).
cnf(304,plain,
is_a_theorem(strict_implies(skc95,skc94)),
inference(sor,[status(thm)],[219,38]),
[iquote('0:SoR:219.0,38.0')] ).
cnf(363,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(strict_implies(not__dfg(u),v)) ),
inference(spr,[status(thm),theory(equality)],[222,151]),
[iquote('0:SpR:222.0,151.1')] ).
cnf(383,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(384,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[149,177]),
[iquote('0:Res:149.0,177.1')] ).
cnf(389,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[158,177]),
[iquote('0:Res:158.0,177.1')] ).
cnf(396,plain,
( ~ is_a_theorem(or__dfg(u,v))
| ~ r3
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[101,177]),
[iquote('0:Res:101.1,177.1')] ).
cnf(399,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[218,177]),
[iquote('0:Res:218.0,177.1')] ).
cnf(400,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(401,plain,
( ~ is_a_theorem(or__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[176,177]),
[iquote('0:Res:176.0,177.1')] ).
cnf(405,plain,
is_a_theorem(skc94),
inference(ssi,[status(thm)],[383,32]),
[iquote('0:SSi:383.0,32.0')] ).
cnf(412,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(426,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(v,u))),
inference(spr,[status(thm),theory(equality)],[178,155]),
[iquote('0:SpR:178.0,155.0')] ).
cnf(427,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(u,v))),
inference(spr,[status(thm),theory(equality)],[178,156]),
[iquote('0:SpR:178.0,156.0')] ).
cnf(554,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[426,177]),
[iquote('0:Res:426.0,177.1')] ).
cnf(556,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(res,[status(thm),theory(equality)],[427,177]),
[iquote('0:Res:427.0,177.1')] ).
cnf(560,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(570,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(implies__dfg(v,w),or__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[168,183]),
[iquote('0:SpR:168.0,183.0')] ).
cnf(573,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(574,plain,
is_a_theorem(implies__dfg(or__dfg(u,v),implies__dfg(implies__dfg(v,w),or__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[168,570]),
[iquote('0:Rew:168.0,570.0')] ).
cnf(1059,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| ~ r5
| is_a_theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[134,177]),
[iquote('0:Res:134.1,177.1')] ).
cnf(1888,plain,
( ~ r3
| is_a_theorem(or__dfg(necessarily(possibly(not__dfg(u))),u)) ),
inference(sor,[status(thm)],[396,205]),
[iquote('0:SoR:396.0,205.0')] ).
cnf(1896,plain,
( ~ r3
| is_a_theorem(strict_implies(not__dfg(necessarily(possibly(not__dfg(u)))),u)) ),
inference(sor,[status(thm)],[363,1888]),
[iquote('0:SoR:363.0,1888.1')] ).
cnf(1907,plain,
( ~ r3
| is_a_theorem(strict_implies(possibly(necessarily(not__dfg(not__dfg(u)))),u)) ),
inference(rew,[status(thm),theory(equality)],[194,1896]),
[iquote('0:Rew:194.0,1896.1')] ).
cnf(1995,plain,
is_a_theorem(implies__dfg(necessarily(skc95),necessarily(skc94))),
inference(sor,[status(thm)],[400,304]),
[iquote('0:SoR:400.0,304.0')] ).
cnf(1997,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(or__dfg(u,v)))),
inference(sor,[status(thm)],[400,299]),
[iquote('0:SoR:400.0,299.0')] ).
cnf(1998,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(implies__dfg(v,u)))),
inference(sor,[status(thm)],[400,298]),
[iquote('0:SoR:400.0,298.0')] ).
cnf(1999,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(necessarily(possibly(u))))),
inference(sor,[status(thm)],[400,301]),
[iquote('0:SoR:400.0,301.0')] ).
cnf(2011,plain,
is_a_theorem(implies__dfg(necessarily(u),strict_implies(not__dfg(u),v))),
inference(rew,[status(thm),theory(equality)],[222,1997]),
[iquote('0:Rew:222.0,1997.0')] ).
cnf(2012,plain,
is_a_theorem(implies__dfg(necessarily(u),strict_implies(v,u))),
inference(rew,[status(thm),theory(equality)],[161,1998]),
[iquote('0:Rew:161.0,1998.0')] ).
cnf(2036,plain,
is_a_theorem(strict_implies(necessarily(skc95),necessarily(skc94))),
inference(sor,[status(thm)],[219,1995]),
[iquote('0:SoR:219.0,1995.0')] ).
cnf(2037,plain,
( ~ is_a_theorem(necessarily(skc95))
| is_a_theorem(necessarily(skc94)) ),
inference(res,[status(thm),theory(equality)],[1995,177]),
[iquote('0:Res:1995.0,177.1')] ).
cnf(2038,plain,
is_a_theorem(necessarily(skc94)),
inference(ssi,[status(thm)],[2037,151,32]),
[iquote('0:SSi:2037.0,151.0,32.1')] ).
cnf(2040,plain,
is_a_theorem(implies__dfg(necessarily(necessarily(skc95)),necessarily(necessarily(skc94)))),
inference(sor,[status(thm)],[400,2036]),
[iquote('0:SoR:400.0,2036.0')] ).
cnf(2046,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[2012,177]),
[iquote('0:Res:2012.0,177.1')] ).
cnf(2056,plain,
( ~ is_a_theorem(necessarily(necessarily(skc95)))
| is_a_theorem(necessarily(necessarily(skc94))) ),
inference(res,[status(thm),theory(equality)],[2040,177]),
[iquote('0:Res:2040.0,177.1')] ).
cnf(2057,plain,
is_a_theorem(necessarily(necessarily(skc94))),
inference(ssi,[status(thm)],[2056,151,32]),
[iquote('0:SSi:2056.0,151.0,151.1,32.1')] ).
cnf(2071,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(necessarily(necessarily(possibly(u)))) ),
inference(res,[status(thm),theory(equality)],[1999,177]),
[iquote('0:Res:1999.0,177.1')] ).
cnf(2110,plain,
is_a_theorem(strict_implies(u,necessarily(skc94))),
inference(sor,[status(thm)],[2046,2057]),
[iquote('0:SoR:2046.0,2057.0')] ).
cnf(2111,plain,
is_a_theorem(strict_implies(u,skc94)),
inference(sor,[status(thm)],[2046,2038]),
[iquote('0:SoR:2046.0,2038.0')] ).
cnf(2116,plain,
is_a_theorem(implies__dfg(u,skc94)),
inference(sor,[status(thm)],[399,2111]),
[iquote('0:SoR:399.0,2111.0')] ).
cnf(2128,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[412,158]),
[iquote('0:SoR:412.0,158.0')] ).
cnf(2181,plain,
is_a_theorem(or__dfg(u,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[168,2128]),
[iquote('0:SpR:168.0,2128.0')] ).
cnf(2202,plain,
is_a_theorem(implies__dfg(u,necessarily(skc94))),
inference(sor,[status(thm)],[399,2110]),
[iquote('0:SoR:399.0,2110.0')] ).
cnf(2247,plain,
( ~ r3
| is_a_theorem(or__dfg(not__dfg(u),u)) ),
inference(sor,[status(thm)],[396,2181]),
[iquote('0:SoR:396.0,2181.0')] ).
cnf(2338,plain,
( ~ r3
| is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))) ),
inference(sor,[status(thm)],[401,2247]),
[iquote('0:SoR:401.0,2247.1')] ).
cnf(2978,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(or__dfg(v,w),or__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[168,574]),
[iquote('0:SpR:168.0,574.0')] ).
cnf(3161,plain,
is_a_theorem(necessarily(necessarily(possibly(skc94)))),
inference(sor,[status(thm)],[2071,2038]),
[iquote('0:SoR:2071.0,2038.0')] ).
cnf(3166,plain,
is_a_theorem(necessarily(possibly(skc94))),
inference(sor,[status(thm)],[384,3161]),
[iquote('0:SoR:384.0,3161.0')] ).
cnf(3168,plain,
is_a_theorem(strict_implies(u,possibly(skc94))),
inference(sor,[status(thm)],[2046,3166]),
[iquote('0:SoR:2046.0,3166.0')] ).
cnf(3198,plain,
is_a_theorem(implies__dfg(u,possibly(skc94))),
inference(sor,[status(thm)],[399,3168]),
[iquote('0:SoR:399.0,3168.0')] ).
cnf(3658,plain,
( ~ r3
| is_a_theorem(implies__dfg(implies__dfg(or__dfg(u,v),or__dfg(v,u)),equiv__dfg(or__dfg(v,u),or__dfg(u,v)))) ),
inference(sor,[status(thm)],[560,101]),
[iquote('0:SoR:560.0,101.1')] ).
cnf(3671,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(u,skc94))),
inference(sor,[status(thm)],[560,2116]),
[iquote('0:SoR:560.0,2116.0')] ).
cnf(3678,plain,
is_a_theorem(implies__dfg(implies__dfg(necessarily(necessarily(u)),necessarily(u)),equiv__dfg(necessarily(u),necessarily(necessarily(u))))),
inference(sor,[status(thm)],[560,160]),
[iquote('0:SoR:560.0,160.0')] ).
cnf(3827,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(v,u))),
inference(sor,[status(thm)],[573,2116]),
[iquote('0:SoR:573.0,2116.0')] ).
cnf(4805,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[3671,177]),
[iquote('0:Res:3671.0,177.1')] ).
cnf(4815,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[412,3827]),
[iquote('0:SoR:412.0,3827.0')] ).
cnf(4839,plain,
is_a_theorem(strict_implies(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[219,4815]),
[iquote('0:SoR:219.0,4815.0')] ).
cnf(4840,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[4815,177]),
[iquote('0:Res:4815.0,177.1')] ).
cnf(4843,plain,
is_a_theorem(implies__dfg(necessarily(implies__dfg(skc94,u)),necessarily(u))),
inference(sor,[status(thm)],[400,4839]),
[iquote('0:SoR:400.0,4839.0')] ).
cnf(4846,plain,
is_a_theorem(implies__dfg(strict_implies(skc94,u),necessarily(u))),
inference(rew,[status(thm),theory(equality)],[161,4843]),
[iquote('0:Rew:161.0,4843.0')] ).
cnf(4869,plain,
( ~ r3
| is_a_theorem(not__dfg(not__dfg(skc94))) ),
inference(sor,[status(thm)],[4840,2338]),
[iquote('0:SoR:4840.0,2338.1')] ).
cnf(4873,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[4840,164]),
[iquote('0:SoR:4840.0,164.0')] ).
cnf(5014,plain,
( ~ r5
| is_a_theorem(implies__dfg(or__dfg(u,strict_implies(v,w)),or__dfg(u,implies__dfg(necessarily(v),necessarily(w))))) ),
inference(sor,[status(thm)],[1059,180]),
[iquote('0:SoR:1059.0,180.0')] ).
cnf(5053,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[219,4873]),
[iquote('0:SoR:219.0,4873.0')] ).
cnf(5122,plain,
( ~ is_a_theorem(strict_implies(skc94,u))
| is_a_theorem(necessarily(u)) ),
inference(res,[status(thm),theory(equality)],[4846,177]),
[iquote('0:Res:4846.0,177.1')] ).
cnf(5500,plain,
is_a_theorem(necessarily(and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[5122,5053]),
[iquote('0:SoR:5122.0,5053.0')] ).
cnf(5515,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[2046,5500]),
[iquote('0:SoR:2046.0,5500.0')] ).
cnf(5520,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[399,5515]),
[iquote('0:SoR:399.0,5515.0')] ).
cnf(8502,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(sor,[status(thm)],[4805,389]),
[iquote('0:SoR:4805.0,389.1')] ).
cnf(8516,plain,
is_a_theorem(equiv__dfg(necessarily(skc94),skc94)),
inference(sor,[status(thm)],[4805,2202]),
[iquote('0:SoR:4805.0,2202.0')] ).
cnf(8540,plain,
is_a_theorem(equiv__dfg(possibly(skc94),skc94)),
inference(sor,[status(thm)],[4805,3198]),
[iquote('0:SoR:4805.0,3198.0')] ).
cnf(8543,plain,
is_a_theorem(equiv__dfg(and__dfg(skc94,skc94),skc94)),
inference(sor,[status(thm)],[4805,5520]),
[iquote('0:SoR:4805.0,5520.0')] ).
cnf(8549,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc94),skc94)),
inference(sor,[status(thm)],[4805,158]),
[iquote('0:SoR:4805.0,158.0')] ).
cnf(8556,plain,
equal(necessarily(skc94),skc94),
inference(res,[status(thm),theory(equality)],[8516,165]),
[iquote('0:Res:8516.0,165.0')] ).
cnf(8889,plain,
equal(possibly(skc94),skc94),
inference(res,[status(thm),theory(equality)],[8540,165]),
[iquote('0:Res:8540.0,165.0')] ).
cnf(10061,plain,
equal(and__dfg(skc94,skc94),skc94),
inference(res,[status(thm),theory(equality)],[8543,165]),
[iquote('0:Res:8543.0,165.0')] ).
cnf(10377,plain,
equal(implies__dfg(u,skc94),skc94),
inference(res,[status(thm),theory(equality)],[8549,165]),
[iquote('0:Res:8549.0,165.0')] ).
cnf(10398,plain,
equal(and__dfg(implies__dfg(skc94,u),skc94),equiv__dfg(skc94,u)),
inference(spr,[status(thm),theory(equality)],[10377,181]),
[iquote('0:SpR:10377.0,181.0')] ).
cnf(10399,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(skc94,equiv__dfg(skc94,u)))),
inference(spr,[status(thm),theory(equality)],[10377,182]),
[iquote('0:SpR:10377.0,182.0')] ).
cnf(10424,plain,
equal(and__dfg(skc94,implies__dfg(skc94,u)),equiv__dfg(u,skc94)),
inference(spr,[status(thm),theory(equality)],[10377,181]),
[iquote('0:SpR:10377.0,181.0')] ).
cnf(11502,plain,
( ~ is_a_theorem(u)
| equal(u,skc94) ),
inference(res,[status(thm),theory(equality)],[8502,165]),
[iquote('0:Res:8502.1,165.0')] ).
cnf(11516,plain,
( ~ r3
| equal(not__dfg(not__dfg(skc94)),skc94) ),
inference(ems,[status(thm)],[11502,4869]),
[iquote('0:EmS:11502.0,4869.1')] ).
cnf(11623,plain,
equal(strict_implies(and__dfg(u,v),v),skc94),
inference(ems,[status(thm)],[11502,295]),
[iquote('0:EmS:11502.0,295.0')] ).
cnf(11625,plain,
equal(strict_implies(implies__dfg(skc94,u),u),skc94),
inference(ems,[status(thm)],[11502,4839]),
[iquote('0:EmS:11502.0,4839.0')] ).
cnf(11632,plain,
equal(strict_implies(and__dfg(u,v),u),skc94),
inference(ems,[status(thm)],[11502,294]),
[iquote('0:EmS:11502.0,294.0')] ).
cnf(11637,plain,
equal(strict_implies(u,and__dfg(skc94,u)),skc94),
inference(ems,[status(thm)],[11502,5053]),
[iquote('0:EmS:11502.0,5053.0')] ).
cnf(11641,plain,
equal(strict_implies(u,implies__dfg(v,u)),skc94),
inference(ems,[status(thm)],[11502,298]),
[iquote('0:EmS:11502.0,298.0')] ).
cnf(11642,plain,
equal(strict_implies(u,necessarily(possibly(u))),skc94),
inference(ems,[status(thm)],[11502,301]),
[iquote('0:EmS:11502.0,301.0')] ).
cnf(11675,plain,
equal(implies__dfg(necessarily(u),strict_implies(not__dfg(u),v)),skc94),
inference(ems,[status(thm)],[11502,2011]),
[iquote('0:EmS:11502.0,2011.0')] ).
cnf(11695,plain,
equal(implies__dfg(or__dfg(u,not__dfg(not__dfg(v))),or__dfg(v,u)),skc94),
inference(ems,[status(thm)],[11502,282]),
[iquote('0:EmS:11502.0,282.0')] ).
cnf(11749,plain,
( ~ r3
| equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc94) ),
inference(ems,[status(thm)],[11502,101]),
[iquote('0:EmS:11502.0,101.1')] ).
cnf(11769,plain,
equal(implies__dfg(necessarily(u),u),skc94),
inference(ems,[status(thm)],[11502,149]),
[iquote('0:EmS:11502.0,149.0')] ).
cnf(11876,plain,
is_a_theorem(implies__dfg(skc94,equiv__dfg(necessarily(u),necessarily(necessarily(u))))),
inference(rew,[status(thm),theory(equality)],[11769,3678]),
[iquote('0:Rew:11769.0,3678.0')] ).
cnf(12278,plain,
( ~ r3
| is_a_theorem(implies__dfg(skc94,equiv__dfg(or__dfg(u,v),or__dfg(v,u)))) ),
inference(rew,[status(thm),theory(equality)],[11749,3658]),
[iquote('0:Rew:11749.1,3658.1')] ).
cnf(12410,plain,
is_a_theorem(equiv__dfg(necessarily(u),necessarily(necessarily(u)))),
inference(sor,[status(thm)],[4840,11876]),
[iquote('0:SoR:4840.0,11876.0')] ).
cnf(12670,plain,
( ~ r3
| equal(not__dfg(and__dfg(u,skc94)),implies__dfg(u,not__dfg(skc94))) ),
inference(spr,[status(thm),theory(equality)],[11516,166]),
[iquote('0:SpR:11516.1,166.0')] ).
cnf(12986,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)],[11625,178]),
[iquote('0:SpR:11625.0,178.0')] ).
cnf(12994,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[11641,12986]),
[iquote('0:Rew:11641.0,12986.0')] ).
cnf(12995,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),skc94),
inference(rew,[status(thm),theory(equality)],[10061,12994]),
[iquote('0:Rew:10061.0,12994.0')] ).
cnf(12999,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)],[11637,178]),
[iquote('0:SpR:11637.0,178.0')] ).
cnf(13006,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[11623,12999]),
[iquote('0:Rew:11623.0,12999.0')] ).
cnf(13007,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[10061,13006]),
[iquote('0:Rew:10061.0,13006.0')] ).
cnf(13171,plain,
equal(necessarily(necessarily(u)),necessarily(u)),
inference(res,[status(thm),theory(equality)],[12410,165]),
[iquote('0:Res:12410.0,165.0')] ).
cnf(13945,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[12995,193]),
[iquote('1:SpL:12995.0,193.0')] ).
cnf(13947,plain,
equal(implies__dfg(skc94,u),u),
inference(mrr,[status(thm)],[13945,405]),
[iquote('1:MRR:13945.0,405.0')] ).
cnf(13964,plain,
( ~ r3
| is_a_theorem(equiv__dfg(or__dfg(u,v),or__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[13947,12278]),
[iquote('1:Rew:13947.0,12278.1')] ).
cnf(13994,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(skc94,u))),
inference(rew,[status(thm),theory(equality)],[13947,10399]),
[iquote('1:Rew:13947.0,10399.0')] ).
cnf(14058,plain,
equal(and__dfg(u,skc94),equiv__dfg(skc94,u)),
inference(rew,[status(thm),theory(equality)],[13947,10398]),
[iquote('1:Rew:13947.0,10398.0')] ).
cnf(14059,plain,
equal(and__dfg(skc94,u),equiv__dfg(u,skc94)),
inference(rew,[status(thm),theory(equality)],[13947,10424]),
[iquote('1:Rew:13947.0,10424.0')] ).
cnf(14109,plain,
( ~ r3
| equal(not__dfg(equiv__dfg(skc94,u)),implies__dfg(u,not__dfg(skc94))) ),
inference(rew,[status(thm),theory(equality)],[14058,12670]),
[iquote('1:Rew:14058.0,12670.1')] ).
cnf(14188,plain,
equal(strict_equiv(u,equiv__dfg(u,skc94)),skc94),
inference(rew,[status(thm),theory(equality)],[14059,13007]),
[iquote('1:Rew:14059.0,13007.0')] ).
cnf(14198,plain,
is_a_theorem(implies__dfg(u,equiv__dfg(skc94,u))),
inference(rew,[status(thm),theory(equality)],[13947,13994]),
[iquote('1:Rew:13947.0,13994.0')] ).
cnf(14268,plain,
equal(strict_implies(skc94,u),necessarily(u)),
inference(spr,[status(thm),theory(equality)],[13947,161]),
[iquote('1:SpR:13947.0,161.0')] ).
cnf(14507,plain,
equal(implies__dfg(u,equiv__dfg(skc94,u)),skc94),
inference(ems,[status(thm)],[11502,14198]),
[iquote('1:EmS:11502.0,14198.0')] ).
cnf(14883,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),implies__dfg(skc94,u)),
inference(spr,[status(thm),theory(equality)],[14059,166]),
[iquote('1:SpR:14059.0,166.0')] ).
cnf(14884,plain,
equal(possibly(equiv__dfg(not__dfg(u),skc94)),not__dfg(strict_implies(skc94,u))),
inference(spr,[status(thm),theory(equality)],[14059,275]),
[iquote('1:SpR:14059.0,275.0')] ).
cnf(14885,plain,
equal(or__dfg(equiv__dfg(not__dfg(u),skc94),v),implies__dfg(implies__dfg(skc94,u),v)),
inference(spr,[status(thm),theory(equality)],[14059,264]),
[iquote('1:SpR:14059.0,264.0')] ).
cnf(14886,plain,
equal(not__dfg(equiv__dfg(possibly(u),skc94)),implies__dfg(skc94,necessarily(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[14059,272]),
[iquote('1:SpR:14059.0,272.0')] ).
cnf(14893,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),u),
inference(rew,[status(thm),theory(equality)],[13947,14883]),
[iquote('1:Rew:13947.0,14883.0')] ).
cnf(14894,plain,
equal(possibly(equiv__dfg(not__dfg(u),skc94)),not__dfg(necessarily(u))),
inference(rew,[status(thm),theory(equality)],[14268,14884]),
[iquote('1:Rew:14268.0,14884.0')] ).
cnf(14895,plain,
equal(not__dfg(equiv__dfg(possibly(u),skc94)),necessarily(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[13947,14886]),
[iquote('1:Rew:13947.0,14886.0')] ).
cnf(14896,plain,
equal(or__dfg(equiv__dfg(not__dfg(u),skc94),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[13947,14885]),
[iquote('1:Rew:13947.0,14885.0')] ).
cnf(15000,plain,
( ~ is_a_theorem(skc94)
| equal(equiv__dfg(u,skc94),u) ),
inference(spl,[status(thm),theory(equality)],[14188,193]),
[iquote('1:SpL:14188.0,193.0')] ).
cnf(15001,plain,
equal(equiv__dfg(u,skc94),u),
inference(mrr,[status(thm)],[15000,405]),
[iquote('1:MRR:15000.0,405.0')] ).
cnf(15003,plain,
equal(and__dfg(skc94,u),u),
inference(rew,[status(thm),theory(equality)],[15001,14059]),
[iquote('1:Rew:15001.0,14059.0')] ).
cnf(15024,plain,
equal(not__dfg(possibly(u)),necessarily(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[15001,14895]),
[iquote('1:Rew:15001.0,14895.0')] ).
cnf(15051,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[15001,14893]),
[iquote('1:Rew:15001.0,14893.0')] ).
cnf(15052,plain,
equal(not__dfg(necessarily(u)),possibly(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[15001,14894]),
[iquote('1:Rew:15001.0,14894.0')] ).
cnf(15053,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[15001,14896]),
[iquote('1:Rew:15001.0,14896.0')] ).
cnf(15144,plain,
( ~ r3
| is_a_theorem(strict_implies(possibly(necessarily(u)),u)) ),
inference(rew,[status(thm),theory(equality)],[15051,1907]),
[iquote('1:Rew:15051.0,1907.1')] ).
cnf(15245,plain,
equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc94),
inference(rew,[status(thm),theory(equality)],[15051,11695]),
[iquote('1:Rew:15051.0,11695.0')] ).
cnf(16338,plain,
( ~ is_a_theorem(skc94)
| r3 ),
inference(rew,[status(thm),theory(equality)],[15245,102]),
[iquote('1:Rew:15245.0,102.0')] ).
cnf(16339,plain,
r3,
inference(mrr,[status(thm)],[16338,405]),
[iquote('1:MRR:16338.0,405.0')] ).
cnf(16467,plain,
is_a_theorem(equiv__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(mrr,[status(thm)],[13964,16339]),
[iquote('1:MRR:13964.0,16339.0')] ).
cnf(16468,plain,
equal(not__dfg(equiv__dfg(skc94,u)),implies__dfg(u,not__dfg(skc94))),
inference(mrr,[status(thm)],[14109,16339]),
[iquote('1:MRR:14109.0,16339.0')] ).
cnf(16471,plain,
is_a_theorem(strict_implies(possibly(necessarily(u)),u)),
inference(mrr,[status(thm)],[15144,16339]),
[iquote('1:MRR:15144.0,16339.0')] ).
cnf(17799,plain,
is_a_theorem(implies__dfg(possibly(necessarily(u)),u)),
inference(sor,[status(thm)],[399,16471]),
[iquote('1:SoR:399.0,16471.0')] ).
cnf(17814,plain,
equal(implies__dfg(possibly(necessarily(u)),u),skc94),
inference(ems,[status(thm)],[11502,17799]),
[iquote('1:EmS:11502.0,17799.0')] ).
cnf(17857,plain,
equal(strict_implies(u,equiv__dfg(skc94,u)),necessarily(skc94)),
inference(spr,[status(thm),theory(equality)],[14507,161]),
[iquote('1:SpR:14507.0,161.0')] ).
cnf(17864,plain,
equal(strict_implies(u,equiv__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[8556,17857]),
[iquote('1:Rew:8556.0,17857.0')] ).
cnf(17872,plain,
equal(implies__dfg(necessarily(not__dfg(u)),v),or__dfg(possibly(u),v)),
inference(spr,[status(thm),theory(equality)],[15024,168]),
[iquote('1:SpR:15024.0,168.0')] ).
cnf(17886,plain,
equal(necessarily(not__dfg(skc94)),not__dfg(skc94)),
inference(spr,[status(thm),theory(equality)],[8889,15024]),
[iquote('1:SpR:8889.0,15024.0')] ).
cnf(18163,plain,
equal(implies__dfg(possibly(necessarily(u)),necessarily(u)),skc94),
inference(spr,[status(thm),theory(equality)],[13171,17814]),
[iquote('1:SpR:13171.0,17814.0')] ).
cnf(18193,plain,
equal(and__dfg(skc94,strict_implies(equiv__dfg(skc94,u),u)),strict_equiv(u,equiv__dfg(skc94,u))),
inference(spr,[status(thm),theory(equality)],[17864,178]),
[iquote('1:SpR:17864.0,178.0')] ).
cnf(18203,plain,
equal(strict_equiv(u,equiv__dfg(skc94,u)),strict_implies(equiv__dfg(skc94,u),u)),
inference(rew,[status(thm),theory(equality)],[15003,18193]),
[iquote('1:Rew:15003.0,18193.0')] ).
cnf(18225,plain,
equal(strict_implies(equiv__dfg(skc94,u),u),skc94),
inference(spr,[status(thm),theory(equality)],[14058,11632]),
[iquote('1:SpR:14058.0,11632.0')] ).
cnf(18232,plain,
equal(strict_equiv(u,equiv__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[18225,18203]),
[iquote('1:Rew:18225.0,18203.0')] ).
cnf(18250,plain,
( ~ is_a_theorem(skc94)
| equal(equiv__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[18232,193]),
[iquote('1:SpL:18232.0,193.0')] ).
cnf(18251,plain,
equal(equiv__dfg(skc94,u),u),
inference(mrr,[status(thm)],[18250,405]),
[iquote('1:MRR:18250.0,405.0')] ).
cnf(18252,plain,
equal(and__dfg(u,skc94),u),
inference(rew,[status(thm),theory(equality)],[18251,14058]),
[iquote('1:Rew:18251.0,14058.0')] ).
cnf(18288,plain,
equal(implies__dfg(u,not__dfg(skc94)),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[18251,16468]),
[iquote('1:Rew:18251.0,16468.0')] ).
cnf(18402,plain,
equal(or__dfg(u,v),or__dfg(v,u)),
inference(res,[status(thm),theory(equality)],[16467,165]),
[iquote('1:Res:16467.0,165.0')] ).
cnf(18415,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(skc147,skc146),implies__dfg(or__dfg(skc147,skc148),or__dfg(skc148,skc146))))
| r5 ),
inference(rew,[status(thm),theory(equality)],[18402,135]),
[iquote('1:Rew:18402.0,135.0')] ).
cnf(18645,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(skc147,skc146),implies__dfg(or__dfg(skc147,skc148),or__dfg(skc146,skc148))))
| r5 ),
inference(rew,[status(thm),theory(equality)],[18402,18415]),
[iquote('1:Rew:18402.0,18415.0')] ).
cnf(19731,plain,
equal(and__dfg(implies__dfg(necessarily(u),possibly(necessarily(u))),skc94),equiv__dfg(necessarily(u),possibly(necessarily(u)))),
inference(spr,[status(thm),theory(equality)],[18163,181]),
[iquote('1:SpR:18163.0,181.0')] ).
cnf(19756,plain,
equal(equiv__dfg(necessarily(u),possibly(necessarily(u))),implies__dfg(necessarily(u),possibly(necessarily(u)))),
inference(rew,[status(thm),theory(equality)],[18252,19731]),
[iquote('1:Rew:18252.0,19731.0')] ).
cnf(22705,plain,
equal(or__dfg(u,not__dfg(v)),implies__dfg(v,u)),
inference(spr,[status(thm),theory(equality)],[15053,18402]),
[iquote('1:SpR:15053.0,18402.0')] ).
cnf(22844,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(u,w),or__dfg(v,w)))),
inference(rew,[status(thm),theory(equality)],[22705,2978]),
[iquote('1:Rew:22705.0,2978.0')] ).
cnf(22940,plain,
r5,
inference(mrr,[status(thm)],[18645,22844]),
[iquote('1:MRR:18645.0,22844.0')] ).
cnf(22976,plain,
is_a_theorem(implies__dfg(or__dfg(u,strict_implies(v,w)),or__dfg(u,implies__dfg(necessarily(v),necessarily(w))))),
inference(mrr,[status(thm)],[5014,22940]),
[iquote('1:MRR:5014.0,22940.0')] ).
cnf(24967,plain,
equal(or__dfg(u,possibly(not__dfg(v))),implies__dfg(necessarily(v),u)),
inference(spr,[status(thm),theory(equality)],[15052,22705]),
[iquote('1:SpR:15052.0,22705.0')] ).
cnf(32497,plain,
equal(implies__dfg(necessarily(not__dfg(u)),strict_implies(u,v)),skc94),
inference(spr,[status(thm),theory(equality)],[15051,11675]),
[iquote('1:SpR:15051.0,11675.0')] ).
cnf(32529,plain,
equal(or__dfg(possibly(u),strict_implies(u,v)),skc94),
inference(rew,[status(thm),theory(equality)],[17872,32497]),
[iquote('1:Rew:17872.0,32497.0')] ).
cnf(44454,plain,
is_a_theorem(implies__dfg(skc94,or__dfg(possibly(u),implies__dfg(necessarily(u),necessarily(v))))),
inference(spr,[status(thm),theory(equality)],[32529,22976]),
[iquote('1:SpR:32529.0,22976.0')] ).
cnf(44471,plain,
is_a_theorem(or__dfg(possibly(u),implies__dfg(necessarily(u),necessarily(v)))),
inference(rew,[status(thm),theory(equality)],[13947,44454]),
[iquote('1:Rew:13947.0,44454.0')] ).
cnf(45179,plain,
is_a_theorem(or__dfg(possibly(u),implies__dfg(necessarily(u),not__dfg(skc94)))),
inference(spr,[status(thm),theory(equality)],[17886,44471]),
[iquote('1:SpR:17886.0,44471.0')] ).
cnf(45248,plain,
is_a_theorem(or__dfg(possibly(u),possibly(not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[15052,45179,18288]),
[iquote('1:Rew:15052.0,45179.0,18288.0,45179.0')] ).
cnf(45249,plain,
is_a_theorem(implies__dfg(necessarily(u),possibly(u))),
inference(rew,[status(thm),theory(equality)],[24967,45248]),
[iquote('1:Rew:24967.0,45248.0')] ).
cnf(45490,plain,
equal(implies__dfg(necessarily(u),possibly(u)),skc94),
inference(ems,[status(thm)],[11502,45249]),
[iquote('1:EmS:11502.0,45249.0')] ).
cnf(45587,plain,
equal(implies__dfg(necessarily(u),possibly(necessarily(u))),skc94),
inference(spr,[status(thm),theory(equality)],[13171,45490]),
[iquote('1:SpR:13171.0,45490.0')] ).
cnf(45599,plain,
equal(equiv__dfg(necessarily(u),possibly(necessarily(u))),skc94),
inference(rew,[status(thm),theory(equality)],[45587,19756]),
[iquote('1:Rew:45587.0,19756.0')] ).
cnf(46102,plain,
( ~ is_a_theorem(skc94)
| equal(possibly(necessarily(u)),necessarily(u)) ),
inference(spl,[status(thm),theory(equality)],[45599,165]),
[iquote('1:SpL:45599.0,165.0')] ).
cnf(46111,plain,
equal(possibly(necessarily(u)),necessarily(u)),
inference(mrr,[status(thm)],[46102,405]),
[iquote('1:MRR:46102.0,405.0')] ).
cnf(47463,plain,
equal(necessarily(not__dfg(necessarily(u))),not__dfg(necessarily(u))),
inference(spr,[status(thm),theory(equality)],[46111,15024]),
[iquote('1:SpR:46111.0,15024.0')] ).
cnf(47498,plain,
equal(necessarily(possibly(not__dfg(u))),possibly(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[15052,47463]),
[iquote('1:Rew:15052.0,47463.0')] ).
cnf(47949,plain,
equal(necessarily(possibly(u)),possibly(u)),
inference(spr,[status(thm),theory(equality)],[15051,47498]),
[iquote('1:SpR:15051.0,47498.0')] ).
cnf(47975,plain,
equal(strict_implies(u,possibly(u)),skc94),
inference(rew,[status(thm),theory(equality)],[47949,11642]),
[iquote('1:Rew:47949.0,11642.0')] ).
cnf(48308,plain,
~ is_a_theorem(skc94),
inference(rew,[status(thm),theory(equality)],[47975,148]),
[iquote('1:Rew:47975.0,148.0')] ).
cnf(48311,plain,
$false,
inference(mrr,[status(thm)],[48308,405]),
[iquote('1:MRR:48308.0,405.0')] ).
cnf(48381,plain,
~ substitution_strict_equiv,
inference(spt,[spt(split,[position(sa)])],[48311,192]),
[iquote('1:Spt:48311.0,44.0,192.0')] ).
cnf(48382,plain,
is_a_theorem(strict_equiv(skc155,skc154)),
inference(spt,[spt(split,[position(s2)])],[44]),
[iquote('1:Spt:48311.0,44.1')] ).
cnf(48385,plain,
~ equal(skc155,skc154),
inference(mrr,[status(thm)],[45,48381]),
[iquote('1:MRR:45.1,48381.0')] ).
cnf(49049,plain,
is_a_theorem(strict_implies(skc155,skc154)),
inference(sor,[status(thm)],[556,48382]),
[iquote('1:SoR:556.0,48382.0')] ).
cnf(49050,plain,
is_a_theorem(strict_implies(skc154,skc155)),
inference(sor,[status(thm)],[554,48382]),
[iquote('1:SoR:554.0,48382.0')] ).
cnf(49062,plain,
is_a_theorem(implies__dfg(skc155,skc154)),
inference(sor,[status(thm)],[399,49049]),
[iquote('1:SoR:399.0,49049.0')] ).
cnf(49097,plain,
is_a_theorem(implies__dfg(skc154,skc155)),
inference(sor,[status(thm)],[399,49050]),
[iquote('1:SoR:399.0,49050.0')] ).
cnf(49100,plain,
equal(implies__dfg(skc155,skc154),skc94),
inference(ems,[status(thm)],[11502,49062]),
[iquote('1:EmS:11502.0,49062.0')] ).
cnf(49105,plain,
equal(implies__dfg(skc154,skc155),skc94),
inference(ems,[status(thm)],[11502,49097]),
[iquote('1:EmS:11502.0,49097.0')] ).
cnf(49146,plain,
equal(and__dfg(implies__dfg(skc154,skc155),skc94),equiv__dfg(skc154,skc155)),
inference(spr,[status(thm),theory(equality)],[49100,181]),
[iquote('1:SpR:49100.0,181.0')] ).
cnf(49155,plain,
equal(and__dfg(skc94,skc94),equiv__dfg(skc154,skc155)),
inference(rew,[status(thm),theory(equality)],[49105,49146]),
[iquote('1:Rew:49105.0,49146.0')] ).
cnf(49156,plain,
equal(equiv__dfg(skc154,skc155),skc94),
inference(rew,[status(thm),theory(equality)],[10061,49155]),
[iquote('1:Rew:10061.0,49155.0')] ).
cnf(49178,plain,
( ~ is_a_theorem(skc94)
| equal(skc155,skc154) ),
inference(spl,[status(thm),theory(equality)],[49156,165]),
[iquote('1:SpL:49156.0,165.0')] ).
cnf(49179,plain,
$false,
inference(mrr,[status(thm)],[49178,405,48385]),
[iquote('1:MRR:49178.0,49178.1,405.0,48385.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL546+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.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 : 600
% 0.12/0.33 % DateTime : Sun Jul 3 13:37:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 17.47/17.71
% 17.47/17.71 SPASS V 3.9
% 17.47/17.71 SPASS beiseite: Proof found.
% 17.47/17.71 % SZS status Theorem
% 17.47/17.71 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.47/17.71 SPASS derived 31265 clauses, backtracked 3251 clauses, performed 3 splits and kept 14137 clauses.
% 17.47/17.71 SPASS allocated 145164 KBytes.
% 17.47/17.71 SPASS spent 0:0:17.33 on the problem.
% 17.47/17.71 0:00:00.04 for the input.
% 17.47/17.71 0:00:00.06 for the FLOTTER CNF translation.
% 17.47/17.71 0:00:00.25 for inferences.
% 17.47/17.71 0:00:01.01 for the backtracking.
% 17.47/17.71 0:0:15.77 for the reduction.
% 17.47/17.71
% 17.47/17.71
% 17.47/17.71 Here is a proof with depth 17, length 291 :
% 17.47/17.71 % SZS output start Refutation
% See solution above
% 19.65/19.86 Formulae used in the proof : s1_0_op_strict_implies s1_0_op_strict_equiv hilbert_op_or hilbert_op_implies_and hilbert_op_equiv hilbert_modus_ponens hilbert_modus_tollens hilbert_implies_1 hilbert_implies_2 hilbert_implies_3 hilbert_and_1 hilbert_and_2 hilbert_and_3 hilbert_or_1 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_m6s3m9b_axiom_m6 modus_ponens axiom_M and_3 substitution_strict_equiv axiom_m6 implies_1 and_1 and_2 or_1 necessitation axiom_B axiom_4 op_possibly r3 op_strict_implies op_implies_and modus_tollens implies_2 op_or op_equiv axiom_K op_strict_equiv implies_3 equivalence_3 r5
% 19.65/19.86
%------------------------------------------------------------------------------