TSTP Solution File: LCL533+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL533+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 14:37:33 EDT 2022
% Result : Theorem 6.55s 6.73s
% Output : Refutation 7.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 59
% Syntax : Number of clauses : 266 ( 164 unt; 1 nHn; 266 RR)
% Number of literals : 377 ( 0 equ; 118 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 31 ( 30 usr; 29 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('LCL533+1.p',unknown),
[] ).
cnf(6,axiom,
op_strict_equiv,
file('LCL533+1.p',unknown),
[] ).
cnf(7,axiom,
op_or,
file('LCL533+1.p',unknown),
[] ).
cnf(8,axiom,
op_implies_and,
file('LCL533+1.p',unknown),
[] ).
cnf(9,axiom,
op_equiv,
file('LCL533+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL533+1.p',unknown),
[] ).
cnf(11,axiom,
modus_tollens,
file('LCL533+1.p',unknown),
[] ).
cnf(12,axiom,
implies_1,
file('LCL533+1.p',unknown),
[] ).
cnf(13,axiom,
implies_2,
file('LCL533+1.p',unknown),
[] ).
cnf(14,axiom,
implies_3,
file('LCL533+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL533+1.p',unknown),
[] ).
cnf(16,axiom,
and_2,
file('LCL533+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL533+1.p',unknown),
[] ).
cnf(18,axiom,
or_1,
file('LCL533+1.p',unknown),
[] ).
cnf(20,axiom,
or_3,
file('LCL533+1.p',unknown),
[] ).
cnf(23,axiom,
equivalence_3,
file('LCL533+1.p',unknown),
[] ).
cnf(24,axiom,
substitution_of_equivalents,
file('LCL533+1.p',unknown),
[] ).
cnf(25,axiom,
op_possibly,
file('LCL533+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL533+1.p',unknown),
[] ).
cnf(27,axiom,
axiom_K,
file('LCL533+1.p',unknown),
[] ).
cnf(28,axiom,
axiom_M,
file('LCL533+1.p',unknown),
[] ).
cnf(29,axiom,
axiom_5,
file('LCL533+1.p',unknown),
[] ).
cnf(30,axiom,
~ axiom_m6,
file('LCL533+1.p',unknown),
[] ).
cnf(31,axiom,
is_a_theorem(skc95),
file('LCL533+1.p',unknown),
[] ).
cnf(37,axiom,
is_a_theorem(implies__dfg(skc95,skc94)),
file('LCL533+1.p',unknown),
[] ).
cnf(43,axiom,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(skc155,skc154)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ equal(skc155,skc154)
| substitution_strict_equiv ),
file('LCL533+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ is_a_theorem(strict_implies(skc181,possibly(skc181)))
| axiom_m6 ),
file('LCL533+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ implies_1
| is_a_theorem(implies__dfg(u,implies__dfg(v,u))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ or_1
| is_a_theorem(implies__dfg(u,or__dfg(u,v))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ kn1
| is_a_theorem(implies__dfg(u,and__dfg(u,u))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ is_a_theorem(implies__dfg(skc126,and__dfg(skc126,skc126)))
| kn1 ),
file('LCL533+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ r1
| is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ is_a_theorem(implies__dfg(or__dfg(skc138,skc138),skc138))
| r1 ),
file('LCL533+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ axiom_B
| is_a_theorem(implies__dfg(u,necessarily(possibly(u)))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ is_a_theorem(implies__dfg(skc160,necessarily(possibly(skc160))))
| axiom_B ),
file('LCL533+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ axiom_5
| is_a_theorem(implies__dfg(possibly(u),necessarily(possibly(u)))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ op_possibly
| equal(not__dfg(necessarily(not__dfg(u))),possibly(u)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL533+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(100,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ is_a_theorem(implies__dfg(or__dfg(skc142,skc141),or__dfg(skc141,skc142)))
| r3 ),
file('LCL533+1.p',unknown),
[] ).
cnf(103,axiom,
( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
file('LCL533+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL533+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ modus_tollens
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(111,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(113,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(119,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ axiom_K
| is_a_theorem(implies__dfg(necessarily(implies__dfg(u,v)),implies__dfg(necessarily(u),necessarily(v)))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(124,axiom,
( ~ op_strict_equiv
| equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)) ),
file('LCL533+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ implies_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(127,axiom,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(141,axiom,
( ~ or_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,v),implies__dfg(or__dfg(u,w),v)))) ),
file('LCL533+1.p',unknown),
[] ).
cnf(147,plain,
~ is_a_theorem(strict_implies(skc181,possibly(skc181))),
inference(mrr,[status(thm)],[49,30]),
[iquote('0:MRR:49.1,30.0')] ).
cnf(148,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[46,28]),
[iquote('0:MRR:46.0,28.0')] ).
cnf(149,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(u)) ),
inference(mrr,[status(thm)],[68,26]),
[iquote('0:MRR:68.1,26.0')] ).
cnf(152,plain,
is_a_theorem(implies__dfg(u,or__dfg(u,v))),
inference(mrr,[status(thm)],[56,18]),
[iquote('0:MRR:56.0,18.0')] ).
cnf(153,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(mrr,[status(thm)],[54,16]),
[iquote('0:MRR:54.0,16.0')] ).
cnf(154,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[52,15]),
[iquote('0:MRR:52.0,15.0')] ).
cnf(156,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(mrr,[status(thm)],[50,12]),
[iquote('0:MRR:50.0,12.0')] ).
cnf(157,plain,
equal(not__dfg(necessarily(not__dfg(u))),possibly(u)),
inference(mrr,[status(thm)],[91,25]),
[iquote('0:MRR:91.0,25.0')] ).
cnf(158,plain,
is_a_theorem(implies__dfg(possibly(u),necessarily(possibly(u)))),
inference(mrr,[status(thm)],[81,29]),
[iquote('0:MRR:81.0,29.0')] ).
cnf(159,plain,
equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
inference(mrr,[status(thm)],[106,4]),
[iquote('0:MRR:106.0,4.0')] ).
cnf(162,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[94,17]),
[iquote('0:MRR:94.0,17.0')] ).
cnf(163,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[93,24]),
[iquote('0:MRR:93.0,24.0')] ).
cnf(164,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[107,8]),
[iquote('0:MRR:107.0,8.0')] ).
cnf(165,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[164,113]),
[iquote('0:Rew:164.0,113.1')] ).
cnf(166,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[165,7]),
[iquote('0:MRR:165.0,7.0')] ).
cnf(172,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[111,13]),
[iquote('0:MRR:111.0,13.0')] ).
cnf(173,plain,
( ~ modus_tollens
| is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[166,109]),
[iquote('0:Rew:166.0,109.1')] ).
cnf(174,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(mrr,[status(thm)],[173,11]),
[iquote('0:MRR:173.0,11.0')] ).
cnf(175,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[108,10]),
[iquote('0:MRR:108.1,10.0')] ).
cnf(176,plain,
equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)),
inference(mrr,[status(thm)],[124,6]),
[iquote('0:MRR:124.0,6.0')] ).
cnf(177,plain,
( ~ axiom_K
| is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(necessarily(u),necessarily(v)))) ),
inference(rew,[status(thm),theory(equality)],[159,120]),
[iquote('0:Rew:159.0,120.1')] ).
cnf(178,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(necessarily(u),necessarily(v)))),
inference(mrr,[status(thm)],[177,27]),
[iquote('0:MRR:177.0,27.0')] ).
cnf(179,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[119,9]),
[iquote('0:MRR:119.0,9.0')] ).
cnf(180,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))),
inference(mrr,[status(thm)],[127,23]),
[iquote('0:MRR:127.0,23.0')] ).
cnf(181,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(mrr,[status(thm)],[125,14]),
[iquote('0:MRR:125.0,14.0')] ).
cnf(185,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,v),implies__dfg(or__dfg(u,w),v)))),
inference(mrr,[status(thm)],[141,20]),
[iquote('0:MRR:141.0,20.0')] ).
cnf(190,plain,
substitution_strict_equiv,
inference(spt,[spt(split,[position(s1)])],[43]),
[iquote('1:Spt:43.0')] ).
cnf(191,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[103,190]),
[iquote('1:MRR:103.0,190.0')] ).
cnf(218,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[159,148]),
[iquote('0:SpR:159.0,148.0')] ).
cnf(219,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(spr,[status(thm),theory(equality)],[159,149]),
[iquote('0:SpR:159.0,149.1')] ).
cnf(263,plain,
equal(not__dfg(necessarily(implies__dfg(u,v))),possibly(and__dfg(u,not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[164,157]),
[iquote('0:SpR:164.0,157.0')] ).
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)],[164,166]),
[iquote('0:SpR:164.0,166.0')] ).
cnf(272,plain,
equal(not__dfg(and__dfg(u,possibly(v))),implies__dfg(u,necessarily(not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[157,164]),
[iquote('0:SpR:157.0,164.0')] ).
cnf(275,plain,
equal(possibly(and__dfg(u,not__dfg(v))),not__dfg(strict_implies(u,v))),
inference(rew,[status(thm),theory(equality)],[159,263]),
[iquote('0:Rew:159.0,263.0')] ).
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)],[166,174]),
[iquote('0:SpR:166.0,174.0')] ).
cnf(294,plain,
( ~ axiom_B
| is_a_theorem(strict_implies(u,necessarily(possibly(u)))) ),
inference(sor,[status(thm)],[219,69]),
[iquote('0:SoR:219.0,69.1')] ).
cnf(295,plain,
is_a_theorem(strict_implies(possibly(u),necessarily(possibly(u)))),
inference(sor,[status(thm)],[219,158]),
[iquote('0:SoR:219.0,158.0')] ).
cnf(296,plain,
( ~ kn1
| is_a_theorem(strict_implies(u,and__dfg(u,u))) ),
inference(sor,[status(thm)],[219,60]),
[iquote('0:SoR:219.0,60.1')] ).
cnf(298,plain,
is_a_theorem(strict_implies(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[219,156]),
[iquote('0:SoR:219.0,156.0')] ).
cnf(301,plain,
is_a_theorem(strict_implies(and__dfg(u,v),u)),
inference(sor,[status(thm)],[219,154]),
[iquote('0:SoR:219.0,154.0')] ).
cnf(303,plain,
is_a_theorem(strict_implies(necessarily(u),u)),
inference(sor,[status(thm)],[219,148]),
[iquote('0:SoR:219.0,148.0')] ).
cnf(304,plain,
is_a_theorem(strict_implies(skc95,skc94)),
inference(sor,[status(thm)],[219,37]),
[iquote('0:SoR:219.0,37.0')] ).
cnf(391,plain,
( ~ is_a_theorem(skc95)
| is_a_theorem(skc94) ),
inference(res,[status(thm),theory(equality)],[37,175]),
[iquote('0:Res:37.0,175.1')] ).
cnf(397,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[156,175]),
[iquote('0:Res:156.0,175.1')] ).
cnf(405,plain,
( ~ is_a_theorem(or__dfg(u,v))
| ~ r3
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[100,175]),
[iquote('0:Res:100.1,175.1')] ).
cnf(408,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[218,175]),
[iquote('0:Res:218.0,175.1')] ).
cnf(409,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(necessarily(u),necessarily(v))) ),
inference(res,[status(thm),theory(equality)],[178,175]),
[iquote('0:Res:178.0,175.1')] ).
cnf(410,plain,
( ~ is_a_theorem(or__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[174,175]),
[iquote('0:Res:174.0,175.1')] ).
cnf(413,plain,
is_a_theorem(skc94),
inference(ssi,[status(thm)],[391,31]),
[iquote('0:SSi:391.0,31.0')] ).
cnf(419,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[172,175]),
[iquote('0:Res:172.0,175.1')] ).
cnf(434,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(v,u))),
inference(spr,[status(thm),theory(equality)],[176,153]),
[iquote('0:SpR:176.0,153.0')] ).
cnf(435,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(u,v))),
inference(spr,[status(thm),theory(equality)],[176,154]),
[iquote('0:SpR:176.0,154.0')] ).
cnf(465,plain,
equal(and__dfg(or__dfg(u,v),implies__dfg(v,not__dfg(u))),equiv__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[166,179]),
[iquote('0:SpR:166.0,179.0')] ).
cnf(534,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[434,175]),
[iquote('0:Res:434.0,175.1')] ).
cnf(562,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(res,[status(thm),theory(equality)],[435,175]),
[iquote('0:Res:435.0,175.1')] ).
cnf(568,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)],[180,175]),
[iquote('0:Res:180.0,175.1')] ).
cnf(579,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)],[181,175]),
[iquote('0:Res:181.0,175.1')] ).
cnf(2061,plain,
is_a_theorem(implies__dfg(necessarily(skc95),necessarily(skc94))),
inference(sor,[status(thm)],[409,304]),
[iquote('0:SoR:409.0,304.0')] ).
cnf(2065,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(implies__dfg(v,u)))),
inference(sor,[status(thm)],[409,298]),
[iquote('0:SoR:409.0,298.0')] ).
cnf(2080,plain,
is_a_theorem(implies__dfg(necessarily(u),strict_implies(v,u))),
inference(rew,[status(thm),theory(equality)],[159,2065]),
[iquote('0:Rew:159.0,2065.0')] ).
cnf(2104,plain,
is_a_theorem(strict_implies(necessarily(skc95),necessarily(skc94))),
inference(sor,[status(thm)],[219,2061]),
[iquote('0:SoR:219.0,2061.0')] ).
cnf(2105,plain,
( ~ is_a_theorem(necessarily(skc95))
| is_a_theorem(necessarily(skc94)) ),
inference(res,[status(thm),theory(equality)],[2061,175]),
[iquote('0:Res:2061.0,175.1')] ).
cnf(2106,plain,
is_a_theorem(necessarily(skc94)),
inference(ssi,[status(thm)],[2105,149,31]),
[iquote('0:SSi:2105.0,149.0,31.1')] ).
cnf(2108,plain,
is_a_theorem(implies__dfg(necessarily(necessarily(skc95)),necessarily(necessarily(skc94)))),
inference(sor,[status(thm)],[409,2104]),
[iquote('0:SoR:409.0,2104.0')] ).
cnf(2114,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[2080,175]),
[iquote('0:Res:2080.0,175.1')] ).
cnf(2124,plain,
( ~ is_a_theorem(necessarily(necessarily(skc95)))
| is_a_theorem(necessarily(necessarily(skc94))) ),
inference(res,[status(thm),theory(equality)],[2108,175]),
[iquote('0:Res:2108.0,175.1')] ).
cnf(2125,plain,
is_a_theorem(necessarily(necessarily(skc94))),
inference(ssi,[status(thm)],[2124,149,31]),
[iquote('0:SSi:2124.0,149.0,149.1,31.1')] ).
cnf(2164,plain,
is_a_theorem(strict_implies(u,skc94)),
inference(sor,[status(thm)],[2114,2106]),
[iquote('0:SoR:2114.0,2106.0')] ).
cnf(2165,plain,
is_a_theorem(strict_implies(u,necessarily(skc94))),
inference(sor,[status(thm)],[2114,2125]),
[iquote('0:SoR:2114.0,2125.0')] ).
cnf(2172,plain,
is_a_theorem(implies__dfg(u,skc94)),
inference(sor,[status(thm)],[408,2164]),
[iquote('0:SoR:408.0,2164.0')] ).
cnf(2185,plain,
is_a_theorem(implies__dfg(u,necessarily(skc94))),
inference(sor,[status(thm)],[408,2165]),
[iquote('0:SoR:408.0,2165.0')] ).
cnf(2189,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(u,u),v))),
inference(sor,[status(thm)],[419,185]),
[iquote('0:SoR:419.0,185.0')] ).
cnf(2193,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(sor,[status(thm)],[419,162]),
[iquote('0:SoR:419.0,162.0')] ).
cnf(2194,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[419,156]),
[iquote('0:SoR:419.0,156.0')] ).
cnf(2198,plain,
kn1,
inference(mrr,[status(thm)],[61,2193]),
[iquote('0:MRR:61.0,2193.0')] ).
cnf(2199,plain,
is_a_theorem(strict_implies(u,and__dfg(u,u))),
inference(mrr,[status(thm)],[296,2198]),
[iquote('0:MRR:296.0,2198.0')] ).
cnf(2242,plain,
is_a_theorem(or__dfg(u,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[166,2194]),
[iquote('0:SpR:166.0,2194.0')] ).
cnf(2304,plain,
( ~ r3
| is_a_theorem(or__dfg(not__dfg(u),u)) ),
inference(sor,[status(thm)],[405,2242]),
[iquote('0:SoR:405.0,2242.0')] ).
cnf(3822,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)],[568,100]),
[iquote('0:SoR:568.0,100.1')] ).
cnf(3845,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(u,skc94))),
inference(sor,[status(thm)],[568,2172]),
[iquote('0:SoR:568.0,2172.0')] ).
cnf(3864,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[3845,175]),
[iquote('0:Res:3845.0,175.1')] ).
cnf(3910,plain,
is_a_theorem(equiv__dfg(and__dfg(skc94,skc94),skc94)),
inference(sor,[status(thm)],[3864,2193]),
[iquote('0:SoR:3864.0,2193.0')] ).
cnf(3912,plain,
is_a_theorem(equiv__dfg(necessarily(skc94),skc94)),
inference(sor,[status(thm)],[3864,2185]),
[iquote('0:SoR:3864.0,2185.0')] ).
cnf(3916,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,and__dfg(skc94,u)),skc94)),
inference(sor,[status(thm)],[3864,162]),
[iquote('0:SoR:3864.0,162.0')] ).
cnf(3917,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc94),skc94)),
inference(sor,[status(thm)],[3864,156]),
[iquote('0:SoR:3864.0,156.0')] ).
cnf(3921,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(sor,[status(thm)],[3864,397]),
[iquote('0:SoR:3864.0,397.1')] ).
cnf(3924,plain,
equal(necessarily(skc94),skc94),
inference(res,[status(thm),theory(equality)],[3912,163]),
[iquote('0:Res:3912.0,163.0')] ).
cnf(4109,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(necessarily(u),v))),
inference(sor,[status(thm)],[579,148]),
[iquote('0:SoR:579.0,148.0')] ).
cnf(4113,plain,
equal(and__dfg(skc94,skc94),skc94),
inference(res,[status(thm),theory(equality)],[3910,163]),
[iquote('0:Res:3910.0,163.0')] ).
cnf(4152,plain,
equal(implies__dfg(u,skc94),skc94),
inference(res,[status(thm),theory(equality)],[3917,163]),
[iquote('0:Res:3917.0,163.0')] ).
cnf(4170,plain,
equal(and__dfg(implies__dfg(skc94,u),skc94),equiv__dfg(skc94,u)),
inference(spr,[status(thm),theory(equality)],[4152,179]),
[iquote('0:SpR:4152.0,179.0')] ).
cnf(4171,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(skc94,equiv__dfg(skc94,u)))),
inference(spr,[status(thm),theory(equality)],[4152,180]),
[iquote('0:SpR:4152.0,180.0')] ).
cnf(4179,plain,
equal(strict_implies(u,skc94),necessarily(skc94)),
inference(spr,[status(thm),theory(equality)],[4152,159]),
[iquote('0:SpR:4152.0,159.0')] ).
cnf(4185,plain,
equal(and__dfg(skc94,implies__dfg(skc94,u)),equiv__dfg(u,skc94)),
inference(spr,[status(thm),theory(equality)],[4152,179]),
[iquote('0:SpR:4152.0,179.0')] ).
cnf(4220,plain,
equal(strict_implies(u,skc94),skc94),
inference(rew,[status(thm),theory(equality)],[3924,4179]),
[iquote('0:Rew:3924.0,4179.0')] ).
cnf(5074,plain,
( ~ is_a_theorem(u)
| equal(u,skc94) ),
inference(res,[status(thm),theory(equality)],[3921,163]),
[iquote('0:Res:3921.1,163.0')] ).
cnf(5096,plain,
( ~ r3
| equal(or__dfg(not__dfg(u),u),skc94) ),
inference(ems,[status(thm)],[5074,2304]),
[iquote('0:EmS:5074.0,2304.1')] ).
cnf(5160,plain,
equal(strict_implies(and__dfg(u,v),u),skc94),
inference(ems,[status(thm)],[5074,301]),
[iquote('0:EmS:5074.0,301.0')] ).
cnf(5162,plain,
equal(strict_implies(u,and__dfg(u,u)),skc94),
inference(ems,[status(thm)],[5074,2199]),
[iquote('0:EmS:5074.0,2199.0')] ).
cnf(5163,plain,
( ~ axiom_B
| equal(strict_implies(u,necessarily(possibly(u))),skc94) ),
inference(ems,[status(thm)],[5074,294]),
[iquote('0:EmS:5074.0,294.1')] ).
cnf(5167,plain,
equal(strict_implies(necessarily(u),u),skc94),
inference(ems,[status(thm)],[5074,303]),
[iquote('0:EmS:5074.0,303.0')] ).
cnf(5177,plain,
equal(strict_implies(possibly(u),necessarily(possibly(u))),skc94),
inference(ems,[status(thm)],[5074,295]),
[iquote('0:EmS:5074.0,295.0')] ).
cnf(5207,plain,
equal(implies__dfg(or__dfg(u,not__dfg(not__dfg(v))),or__dfg(v,u)),skc94),
inference(ems,[status(thm)],[5074,282]),
[iquote('0:EmS:5074.0,282.0')] ).
cnf(5234,plain,
( ~ r3
| equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc94) ),
inference(ems,[status(thm)],[5074,100]),
[iquote('0:EmS:5074.0,100.1')] ).
cnf(5235,plain,
( ~ r1
| equal(implies__dfg(or__dfg(u,u),u),skc94) ),
inference(ems,[status(thm)],[5074,64]),
[iquote('0:EmS:5074.0,64.1')] ).
cnf(5251,plain,
equal(implies__dfg(u,u),skc94),
inference(ems,[status(thm)],[5074,2194]),
[iquote('0:EmS:5074.0,2194.0')] ).
cnf(5253,plain,
equal(implies__dfg(u,implies__dfg(v,u)),skc94),
inference(ems,[status(thm)],[5074,156]),
[iquote('0:EmS:5074.0,156.0')] ).
cnf(5254,plain,
equal(implies__dfg(u,or__dfg(u,v)),skc94),
inference(ems,[status(thm)],[5074,152]),
[iquote('0:EmS:5074.0,152.0')] ).
cnf(5257,plain,
equal(implies__dfg(and__dfg(u,v),u),skc94),
inference(ems,[status(thm)],[5074,154]),
[iquote('0:EmS:5074.0,154.0')] ).
cnf(5258,plain,
equal(implies__dfg(and__dfg(u,v),v),skc94),
inference(ems,[status(thm)],[5074,153]),
[iquote('0:EmS:5074.0,153.0')] ).
cnf(5523,plain,
( ~ r3
| is_a_theorem(implies__dfg(skc94,equiv__dfg(or__dfg(u,v),or__dfg(v,u)))) ),
inference(rew,[status(thm),theory(equality)],[5234,3822]),
[iquote('0:Rew:5234.1,3822.1')] ).
cnf(5867,plain,
equal(and__dfg(skc94,strict_implies(and__dfg(u,u),u)),strict_equiv(u,and__dfg(u,u))),
inference(spr,[status(thm),theory(equality)],[5162,176]),
[iquote('0:SpR:5162.0,176.0')] ).
cnf(5878,plain,
equal(strict_equiv(u,and__dfg(u,u)),skc94),
inference(rew,[status(thm),theory(equality)],[4113,5867,5160]),
[iquote('0:Rew:4113.0,5867.0,5160.0,5867.0')] ).
cnf(6120,plain,
( ~ is_a_theorem(skc94)
| equal(and__dfg(u,u),u) ),
inference(spl,[status(thm),theory(equality)],[5878,191]),
[iquote('1:SpL:5878.0,191.0')] ).
cnf(6121,plain,
equal(and__dfg(u,u),u),
inference(mrr,[status(thm)],[6120,413]),
[iquote('1:MRR:6120.0,413.0')] ).
cnf(6189,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),u),v),or__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[6121,264]),
[iquote('1:SpR:6121.0,264.0')] ).
cnf(6204,plain,
equal(implies__dfg(or__dfg(u,u),v),or__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[166,6189]),
[iquote('1:Rew:166.0,6189.0')] ).
cnf(6206,plain,
( ~ is_a_theorem(or__dfg(not__dfg(skc138),skc138))
| r1 ),
inference(rew,[status(thm),theory(equality)],[6204,65]),
[iquote('1:Rew:6204.0,65.0')] ).
cnf(6207,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),or__dfg(not__dfg(u),v))),
inference(rew,[status(thm),theory(equality)],[6204,2189]),
[iquote('1:Rew:6204.0,2189.0')] ).
cnf(6210,plain,
( ~ r1
| equal(or__dfg(not__dfg(u),u),skc94) ),
inference(rew,[status(thm),theory(equality)],[6204,5235]),
[iquote('1:Rew:6204.0,5235.1')] ).
cnf(6547,plain,
equal(implies__dfg(u,and__dfg(skc94,u)),skc94),
inference(res,[status(thm),theory(equality)],[3916,163]),
[iquote('0:Res:3916.0,163.0')] ).
cnf(6555,plain,
equal(and__dfg(implies__dfg(and__dfg(skc94,u),u),skc94),equiv__dfg(and__dfg(skc94,u),u)),
inference(spr,[status(thm),theory(equality)],[6547,179]),
[iquote('0:SpR:6547.0,179.0')] ).
cnf(6571,plain,
equal(equiv__dfg(and__dfg(skc94,u),u),skc94),
inference(rew,[status(thm),theory(equality)],[6121,6555,5258]),
[iquote('1:Rew:6121.0,6555.0,5258.0,6555.0')] ).
cnf(6593,plain,
( ~ is_a_theorem(skc94)
| equal(and__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[6571,163]),
[iquote('1:SpL:6571.0,163.0')] ).
cnf(6594,plain,
equal(and__dfg(skc94,u),u),
inference(mrr,[status(thm)],[6593,413]),
[iquote('1:MRR:6593.0,413.0')] ).
cnf(6607,plain,
equal(equiv__dfg(u,skc94),implies__dfg(skc94,u)),
inference(rew,[status(thm),theory(equality)],[6594,4185]),
[iquote('1:Rew:6594.0,4185.0')] ).
cnf(6759,plain,
equal(not__dfg(not__dfg(u)),implies__dfg(skc94,u)),
inference(spr,[status(thm),theory(equality)],[6594,164]),
[iquote('1:SpR:6594.0,164.0')] ).
cnf(6760,plain,
equal(not__dfg(strict_implies(skc94,u)),possibly(not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[6594,275]),
[iquote('1:SpR:6594.0,275.0')] ).
cnf(6761,plain,
equal(implies__dfg(implies__dfg(skc94,u),v),or__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[6594,264]),
[iquote('1:SpR:6594.0,264.0')] ).
cnf(6762,plain,
equal(implies__dfg(skc94,necessarily(not__dfg(u))),not__dfg(possibly(u))),
inference(spr,[status(thm),theory(equality)],[6594,272]),
[iquote('1:SpR:6594.0,272.0')] ).
cnf(6857,plain,
equal(implies__dfg(or__dfg(u,implies__dfg(skc94,v)),or__dfg(v,u)),skc94),
inference(rew,[status(thm),theory(equality)],[6759,5207]),
[iquote('1:Rew:6759.0,5207.0')] ).
cnf(6910,plain,
is_a_theorem(or__dfg(not__dfg(u),implies__dfg(skc94,equiv__dfg(skc94,u)))),
inference(rew,[status(thm),theory(equality)],[6761,4171]),
[iquote('1:Rew:6761.0,4171.0')] ).
cnf(6951,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| equal(u,skc94) ),
inference(spl,[status(thm),theory(equality)],[6607,163]),
[iquote('1:SpL:6607.0,163.0')] ).
cnf(7255,plain,
( ~ r3
| equal(and__dfg(skc94,implies__dfg(u,not__dfg(not__dfg(u)))),equiv__dfg(not__dfg(not__dfg(u)),u)) ),
inference(spr,[status(thm),theory(equality)],[5096,465]),
[iquote('0:SpR:5096.1,465.0')] ).
cnf(7295,plain,
( ~ r3
| equal(equiv__dfg(implies__dfg(skc94,u),u),skc94) ),
inference(rew,[status(thm),theory(equality)],[5253,7255,6594,6759]),
[iquote('1:Rew:5253.0,7255.1,6594.0,7255.1,6759.0,7255.1')] ).
cnf(7304,plain,
equal(and__dfg(skc94,strict_implies(necessarily(possibly(u)),possibly(u))),strict_equiv(possibly(u),necessarily(possibly(u)))),
inference(spr,[status(thm),theory(equality)],[5177,176]),
[iquote('0:SpR:5177.0,176.0')] ).
cnf(7319,plain,
equal(strict_equiv(possibly(u),necessarily(possibly(u))),skc94),
inference(rew,[status(thm),theory(equality)],[6594,7304,5167]),
[iquote('1:Rew:6594.0,7304.0,5167.0,7304.0')] ).
cnf(7403,plain,
( ~ r1
| equal(and__dfg(skc94,implies__dfg(u,not__dfg(not__dfg(u)))),equiv__dfg(not__dfg(not__dfg(u)),u)) ),
inference(spr,[status(thm),theory(equality)],[6210,465]),
[iquote('1:SpR:6210.1,465.0')] ).
cnf(7441,plain,
( ~ r1
| equal(equiv__dfg(implies__dfg(skc94,u),u),skc94) ),
inference(rew,[status(thm),theory(equality)],[5253,7403,6594,6759]),
[iquote('1:Rew:5253.0,7403.1,6594.0,7403.1,6759.0,7403.1')] ).
cnf(7550,plain,
equal(possibly(not__dfg(skc94)),not__dfg(skc94)),
inference(spr,[status(thm),theory(equality)],[4220,6760]),
[iquote('1:SpR:4220.0,6760.0')] ).
cnf(7766,plain,
( ~ is_a_theorem(skc94)
| equal(necessarily(possibly(u)),possibly(u)) ),
inference(spl,[status(thm),theory(equality)],[7319,191]),
[iquote('1:SpL:7319.0,191.0')] ).
cnf(7771,plain,
equal(necessarily(possibly(u)),possibly(u)),
inference(mrr,[status(thm)],[7766,413]),
[iquote('1:MRR:7766.0,413.0')] ).
cnf(7773,plain,
( ~ is_a_theorem(implies__dfg(skc160,possibly(skc160)))
| axiom_B ),
inference(rew,[status(thm),theory(equality)],[7771,70]),
[iquote('1:Rew:7771.0,70.0')] ).
cnf(7910,plain,
( ~ axiom_B
| equal(strict_implies(u,possibly(u)),skc94) ),
inference(rew,[status(thm),theory(equality)],[7771,5163]),
[iquote('1:Rew:7771.0,5163.1')] ).
cnf(8209,plain,
equal(necessarily(not__dfg(skc94)),not__dfg(skc94)),
inference(spr,[status(thm),theory(equality)],[7550,7771]),
[iquote('1:SpR:7550.0,7771.0')] ).
cnf(8316,plain,
equal(not__dfg(not__dfg(skc94)),possibly(skc94)),
inference(spr,[status(thm),theory(equality)],[8209,157]),
[iquote('1:SpR:8209.0,157.0')] ).
cnf(8321,plain,
equal(possibly(skc94),skc94),
inference(rew,[status(thm),theory(equality)],[5251,8316,6759]),
[iquote('1:Rew:5251.0,8316.0,6759.0,8316.0')] ).
cnf(8366,plain,
equal(implies__dfg(u,necessarily(not__dfg(skc94))),not__dfg(and__dfg(u,skc94))),
inference(spr,[status(thm),theory(equality)],[8321,272]),
[iquote('1:SpR:8321.0,272.0')] ).
cnf(8370,plain,
equal(not__dfg(and__dfg(u,skc94)),implies__dfg(u,not__dfg(skc94))),
inference(rew,[status(thm),theory(equality)],[8209,8366]),
[iquote('1:Rew:8209.0,8366.0')] ).
cnf(8677,plain,
( ~ axiom_B
| ~ is_a_theorem(skc94) ),
inference(spl,[status(thm),theory(equality)],[7910,147]),
[iquote('1:SpL:7910.1,147.0')] ).
cnf(8680,plain,
~ axiom_B,
inference(mrr,[status(thm)],[8677,413]),
[iquote('1:MRR:8677.1,413.0')] ).
cnf(8683,plain,
~ is_a_theorem(implies__dfg(skc160,possibly(skc160))),
inference(mrr,[status(thm)],[7773,8680]),
[iquote('1:MRR:7773.1,8680.0')] ).
cnf(12229,plain,
( ~ r3
| is_a_theorem(or__dfg(implies__dfg(skc94,equiv__dfg(skc94,u)),not__dfg(u))) ),
inference(sor,[status(thm)],[405,6910]),
[iquote('1:SoR:405.0,6910.0')] ).
cnf(12497,plain,
( ~ r3
| ~ is_a_theorem(skc94)
| equal(implies__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[7295,163]),
[iquote('1:SpL:7295.1,163.0')] ).
cnf(12502,plain,
( ~ r3
| equal(implies__dfg(skc94,u),u) ),
inference(mrr,[status(thm)],[12497,413]),
[iquote('1:MRR:12497.1,413.0')] ).
cnf(12506,plain,
( ~ r3
| is_a_theorem(or__dfg(equiv__dfg(skc94,u),not__dfg(u))) ),
inference(rew,[status(thm),theory(equality)],[12502,12229]),
[iquote('1:Rew:12502.1,12229.1')] ).
cnf(12507,plain,
( ~ r3
| is_a_theorem(equiv__dfg(or__dfg(u,v),or__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[12502,5523]),
[iquote('1:Rew:12502.1,5523.1')] ).
cnf(12532,plain,
( ~ r3
| equal(and__dfg(u,skc94),equiv__dfg(skc94,u)) ),
inference(spr,[status(thm),theory(equality)],[12502,4170]),
[iquote('1:SpR:12502.1,4170.0')] ).
cnf(12545,plain,
( ~ r3
| equal(not__dfg(possibly(u)),necessarily(not__dfg(u))) ),
inference(spr,[status(thm),theory(equality)],[12502,6762]),
[iquote('1:SpR:12502.1,6762.0')] ).
cnf(13921,plain,
( ~ r1
| ~ is_a_theorem(skc94)
| equal(implies__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[7441,163]),
[iquote('1:SpL:7441.1,163.0')] ).
cnf(13926,plain,
( ~ r1
| equal(implies__dfg(skc94,u),u) ),
inference(mrr,[status(thm)],[13921,413]),
[iquote('1:MRR:13921.1,413.0')] ).
cnf(16093,plain,
( ~ r3
| is_a_theorem(implies__dfg(u,equiv__dfg(skc94,u))) ),
inference(sor,[status(thm)],[410,12506]),
[iquote('1:SoR:410.0,12506.1')] ).
cnf(16314,plain,
( ~ r3
| is_a_theorem(implies__dfg(implies__dfg(equiv__dfg(skc94,u),u),equiv__dfg(u,equiv__dfg(skc94,u)))) ),
inference(sor,[status(thm)],[568,16093]),
[iquote('1:SoR:568.0,16093.1')] ).
cnf(16350,plain,
( ~ r3
| equal(implies__dfg(equiv__dfg(skc94,u),u),skc94) ),
inference(spr,[status(thm),theory(equality)],[12532,5257]),
[iquote('1:SpR:12532.1,5257.0')] ).
cnf(16353,plain,
( ~ r3
| equal(not__dfg(equiv__dfg(skc94,u)),implies__dfg(u,not__dfg(skc94))) ),
inference(spr,[status(thm),theory(equality)],[12532,8370]),
[iquote('1:SpR:12532.1,8370.0')] ).
cnf(16361,plain,
( ~ r3
| is_a_theorem(implies__dfg(skc94,equiv__dfg(u,equiv__dfg(skc94,u)))) ),
inference(rew,[status(thm),theory(equality)],[16350,16314]),
[iquote('1:Rew:16350.1,16314.1')] ).
cnf(16362,plain,
( ~ r3
| is_a_theorem(equiv__dfg(u,equiv__dfg(skc94,u))) ),
inference(rew,[status(thm),theory(equality)],[12502,16361]),
[iquote('1:Rew:12502.1,16361.1')] ).
cnf(16378,plain,
( ~ r3
| equal(equiv__dfg(skc94,u),u) ),
inference(res,[status(thm),theory(equality)],[16362,163]),
[iquote('1:Res:16362.1,163.0')] ).
cnf(16398,plain,
( ~ r3
| equal(implies__dfg(u,not__dfg(skc94)),not__dfg(u)) ),
inference(rew,[status(thm),theory(equality)],[16378,16353]),
[iquote('1:Rew:16378.1,16353.1')] ).
cnf(16647,plain,
( ~ r3
| equal(implies__dfg(necessarily(not__dfg(u)),v),or__dfg(possibly(u),v)) ),
inference(spr,[status(thm),theory(equality)],[12545,166]),
[iquote('1:SpR:12545.1,166.0')] ).
cnf(16829,plain,
is_a_theorem(implies__dfg(skc94,implies__dfg(necessarily(u),or__dfg(u,v)))),
inference(spr,[status(thm),theory(equality)],[5254,4109]),
[iquote('0:SpR:5254.0,4109.0')] ).
cnf(17026,plain,
is_a_theorem(implies__dfg(skc94,or__dfg(not__dfg(u),u))),
inference(spr,[status(thm),theory(equality)],[5251,6207]),
[iquote('1:SpR:5251.0,6207.0')] ).
cnf(17166,plain,
equal(or__dfg(not__dfg(u),u),skc94),
inference(res,[status(thm),theory(equality)],[17026,6951]),
[iquote('1:Res:17026.0,6951.0')] ).
cnf(17178,plain,
( ~ is_a_theorem(skc94)
| r1 ),
inference(rew,[status(thm),theory(equality)],[17166,6206]),
[iquote('1:Rew:17166.0,6206.0')] ).
cnf(17183,plain,
r1,
inference(mrr,[status(thm)],[17178,413]),
[iquote('1:MRR:17178.0,413.0')] ).
cnf(17186,plain,
equal(implies__dfg(skc94,u),u),
inference(mrr,[status(thm)],[13926,17183]),
[iquote('1:MRR:13926.0,17183.0')] ).
cnf(17330,plain,
equal(implies__dfg(or__dfg(u,v),or__dfg(v,u)),skc94),
inference(rew,[status(thm),theory(equality)],[17186,6857]),
[iquote('1:Rew:17186.0,6857.0')] ).
cnf(17350,plain,
is_a_theorem(implies__dfg(necessarily(u),or__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[17186,16829]),
[iquote('1:Rew:17186.0,16829.0')] ).
cnf(17422,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[17186,6761]),
[iquote('1:Rew:17186.0,6761.0')] ).
cnf(18119,plain,
( ~ is_a_theorem(skc94)
| r3 ),
inference(rew,[status(thm),theory(equality)],[17330,101]),
[iquote('1:Rew:17330.0,101.0')] ).
cnf(18121,plain,
r3,
inference(mrr,[status(thm)],[18119,413]),
[iquote('1:MRR:18119.0,413.0')] ).
cnf(18187,plain,
is_a_theorem(equiv__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(mrr,[status(thm)],[12507,18121]),
[iquote('1:MRR:12507.0,18121.0')] ).
cnf(18203,plain,
equal(implies__dfg(u,not__dfg(skc94)),not__dfg(u)),
inference(mrr,[status(thm)],[16398,18121]),
[iquote('1:MRR:16398.0,18121.0')] ).
cnf(18210,plain,
equal(implies__dfg(necessarily(not__dfg(u)),v),or__dfg(possibly(u),v)),
inference(mrr,[status(thm)],[16647,18121]),
[iquote('1:MRR:16647.0,18121.0')] ).
cnf(19636,plain,
equal(implies__dfg(necessarily(u),or__dfg(u,v)),skc94),
inference(ems,[status(thm)],[5074,17350]),
[iquote('1:EmS:5074.0,17350.0')] ).
cnf(19713,plain,
equal(or__dfg(u,v),or__dfg(v,u)),
inference(res,[status(thm),theory(equality)],[18187,163]),
[iquote('1:Res:18187.0,163.0')] ).
cnf(23354,plain,
equal(or__dfg(u,not__dfg(v)),implies__dfg(v,u)),
inference(spr,[status(thm),theory(equality)],[17422,19713]),
[iquote('1:SpR:17422.0,19713.0')] ).
cnf(23365,plain,
equal(implies__dfg(necessarily(not__dfg(u)),implies__dfg(u,v)),skc94),
inference(spr,[status(thm),theory(equality)],[17422,19636]),
[iquote('1:SpR:17422.0,19636.0')] ).
cnf(23560,plain,
equal(or__dfg(possibly(u),implies__dfg(u,v)),skc94),
inference(rew,[status(thm),theory(equality)],[18210,23365]),
[iquote('1:Rew:18210.0,23365.0')] ).
cnf(23753,plain,
equal(or__dfg(possibly(u),not__dfg(u)),skc94),
inference(spr,[status(thm),theory(equality)],[18203,23560]),
[iquote('1:SpR:18203.0,23560.0')] ).
cnf(23763,plain,
equal(implies__dfg(u,possibly(u)),skc94),
inference(rew,[status(thm),theory(equality)],[23354,23753]),
[iquote('1:Rew:23354.0,23753.0')] ).
cnf(23764,plain,
~ is_a_theorem(skc94),
inference(rew,[status(thm),theory(equality)],[23763,8683]),
[iquote('1:Rew:23763.0,8683.0')] ).
cnf(23767,plain,
$false,
inference(mrr,[status(thm)],[23764,413]),
[iquote('1:MRR:23764.0,413.0')] ).
cnf(23775,plain,
~ substitution_strict_equiv,
inference(spt,[spt(split,[position(sa)])],[23767,190]),
[iquote('1:Spt:23767.0,43.0,190.0')] ).
cnf(23776,plain,
is_a_theorem(strict_equiv(skc155,skc154)),
inference(spt,[spt(split,[position(s2)])],[43]),
[iquote('1:Spt:23767.0,43.1')] ).
cnf(23779,plain,
~ equal(skc155,skc154),
inference(mrr,[status(thm)],[44,23775]),
[iquote('1:MRR:44.1,23775.0')] ).
cnf(24035,plain,
is_a_theorem(strict_implies(skc155,skc154)),
inference(sor,[status(thm)],[562,23776]),
[iquote('1:SoR:562.0,23776.0')] ).
cnf(24036,plain,
is_a_theorem(strict_implies(skc154,skc155)),
inference(sor,[status(thm)],[534,23776]),
[iquote('1:SoR:534.0,23776.0')] ).
cnf(24066,plain,
is_a_theorem(implies__dfg(skc155,skc154)),
inference(sor,[status(thm)],[408,24035]),
[iquote('1:SoR:408.0,24035.0')] ).
cnf(24071,plain,
is_a_theorem(implies__dfg(skc154,skc155)),
inference(sor,[status(thm)],[408,24036]),
[iquote('1:SoR:408.0,24036.0')] ).
cnf(24077,plain,
equal(implies__dfg(skc155,skc154),skc94),
inference(ems,[status(thm)],[5074,24066]),
[iquote('1:EmS:5074.0,24066.0')] ).
cnf(24083,plain,
equal(implies__dfg(skc154,skc155),skc94),
inference(ems,[status(thm)],[5074,24071]),
[iquote('1:EmS:5074.0,24071.0')] ).
cnf(24118,plain,
equal(and__dfg(implies__dfg(skc154,skc155),skc94),equiv__dfg(skc154,skc155)),
inference(spr,[status(thm),theory(equality)],[24077,179]),
[iquote('1:SpR:24077.0,179.0')] ).
cnf(24126,plain,
equal(and__dfg(skc94,skc94),equiv__dfg(skc154,skc155)),
inference(rew,[status(thm),theory(equality)],[24083,24118]),
[iquote('1:Rew:24083.0,24118.0')] ).
cnf(24127,plain,
equal(equiv__dfg(skc154,skc155),skc94),
inference(rew,[status(thm),theory(equality)],[4113,24126]),
[iquote('1:Rew:4113.0,24126.0')] ).
cnf(24150,plain,
( ~ is_a_theorem(skc94)
| equal(skc155,skc154) ),
inference(spl,[status(thm),theory(equality)],[24127,163]),
[iquote('1:SpL:24127.0,163.0')] ).
cnf(24151,plain,
$false,
inference(mrr,[status(thm)],[24150,413,23779]),
[iquote('1:MRR:24150.0,24150.1,413.0,23779.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL533+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 20:23:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.55/6.73
% 6.55/6.73 SPASS V 3.9
% 6.55/6.73 SPASS beiseite: Proof found.
% 6.55/6.73 % SZS status Theorem
% 6.55/6.73 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.55/6.73 SPASS derived 16117 clauses, backtracked 2020 clauses, performed 3 splits and kept 8854 clauses.
% 6.55/6.73 SPASS allocated 123855 KBytes.
% 6.55/6.73 SPASS spent 0:00:06.37 on the problem.
% 6.55/6.73 0:00:00.04 for the input.
% 6.55/6.73 0:00:00.06 for the FLOTTER CNF translation.
% 6.55/6.73 0:00:00.12 for inferences.
% 6.55/6.73 0:00:00.24 for the backtracking.
% 6.55/6.73 0:00:05.82 for the reduction.
% 6.55/6.73
% 6.55/6.73
% 6.55/6.73 Here is a proof with depth 19, length 266 :
% 6.55/6.73 % SZS output start Refutation
% See solution above
% 7.24/7.43 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_or_3 hilbert_equivalence_3 substitution_of_equivalents km5_op_possibly km5_necessitation km5_axiom_K km5_axiom_M km5_axiom_5 s1_0_m6s3m9b_axiom_m6 modus_ponens axiom_M and_3 substitution_strict_equiv axiom_m6 implies_1 and_1 and_2 or_1 kn1 r1 necessitation axiom_B axiom_5 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 or_3
% 7.24/7.43
%------------------------------------------------------------------------------