TSTP Solution File: LCL535+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL535+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 6.70s 6.92s
% Output : Refutation 7.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 43
% Syntax : Number of clauses : 160 ( 113 unt; 1 nHn; 160 RR)
% Number of literals : 213 ( 0 equ; 58 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 23 ( 22 usr; 21 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
op_strict_implies,
file('LCL535+1.p',unknown),
[] ).
cnf(6,axiom,
op_strict_equiv,
file('LCL535+1.p',unknown),
[] ).
cnf(8,axiom,
op_implies_and,
file('LCL535+1.p',unknown),
[] ).
cnf(9,axiom,
op_equiv,
file('LCL535+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL535+1.p',unknown),
[] ).
cnf(12,axiom,
implies_1,
file('LCL535+1.p',unknown),
[] ).
cnf(13,axiom,
implies_2,
file('LCL535+1.p',unknown),
[] ).
cnf(14,axiom,
implies_3,
file('LCL535+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL535+1.p',unknown),
[] ).
cnf(16,axiom,
and_2,
file('LCL535+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL535+1.p',unknown),
[] ).
cnf(23,axiom,
equivalence_3,
file('LCL535+1.p',unknown),
[] ).
cnf(24,axiom,
substitution_of_equivalents,
file('LCL535+1.p',unknown),
[] ).
cnf(25,axiom,
op_possibly,
file('LCL535+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL535+1.p',unknown),
[] ).
cnf(27,axiom,
axiom_K,
file('LCL535+1.p',unknown),
[] ).
cnf(28,axiom,
axiom_M,
file('LCL535+1.p',unknown),
[] ).
cnf(29,axiom,
axiom_5,
file('LCL535+1.p',unknown),
[] ).
cnf(30,axiom,
~ axiom_m9,
file('LCL535+1.p',unknown),
[] ).
cnf(31,axiom,
is_a_theorem(skc95),
file('LCL535+1.p',unknown),
[] ).
cnf(37,axiom,
is_a_theorem(implies__dfg(skc95,skc94)),
file('LCL535+1.p',unknown),
[] ).
cnf(43,axiom,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(skc155,skc154)) ),
file('LCL535+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ equal(skc155,skc154)
| substitution_strict_equiv ),
file('LCL535+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL535+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ implies_1
| is_a_theorem(implies__dfg(u,implies__dfg(v,u))) ),
file('LCL535+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL535+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL535+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL535+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ axiom_5
| is_a_theorem(implies__dfg(possibly(u),necessarily(possibly(u)))) ),
file('LCL535+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ is_a_theorem(strict_implies(possibly(possibly(skc186)),possibly(skc186)))
| axiom_m9 ),
file('LCL535+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ op_possibly
| equal(not__dfg(necessarily(not__dfg(u))),possibly(u)) ),
file('LCL535+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL535+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL535+1.p',unknown),
[] ).
cnf(103,axiom,
( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(u,v))
| equal(u,v) ),
file('LCL535+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL535+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL535+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL535+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('LCL535+1.p',unknown),
[] ).
cnf(119,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL535+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('LCL535+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('LCL535+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('LCL535+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('LCL535+1.p',unknown),
[] ).
cnf(147,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[46,28]),
[iquote('0:MRR:46.0,28.0')] ).
cnf(148,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(and__dfg(u,v),v)),
inference(mrr,[status(thm)],[54,16]),
[iquote('0:MRR:54.0,16.0')] ).
cnf(153,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(155,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(156,plain,
equal(not__dfg(necessarily(not__dfg(u))),possibly(u)),
inference(mrr,[status(thm)],[91,25]),
[iquote('0:MRR:91.0,25.0')] ).
cnf(157,plain,
~ is_a_theorem(strict_implies(possibly(possibly(skc186)),possibly(skc186))),
inference(mrr,[status(thm)],[88,30]),
[iquote('0:MRR:88.1,30.0')] ).
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(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(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(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(192,plain,
equal(not__dfg(necessarily(possibly(u))),possibly(necessarily(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[156]),
[iquote('0:SpR:156.0,156.0')] ).
cnf(214,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[159,147]),
[iquote('0:SpR:159.0,147.0')] ).
cnf(215,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(spr,[status(thm),theory(equality)],[159,148]),
[iquote('0:SpR:159.0,148.1')] ).
cnf(298,plain,
is_a_theorem(strict_implies(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[215,155]),
[iquote('0:SoR:215.0,155.0')] ).
cnf(302,plain,
is_a_theorem(strict_implies(and__dfg(u,v),v)),
inference(sor,[status(thm)],[215,152]),
[iquote('0:SoR:215.0,152.0')] ).
cnf(304,plain,
is_a_theorem(strict_implies(skc95,skc94)),
inference(sor,[status(thm)],[215,37]),
[iquote('0:SoR:215.0,37.0')] ).
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)],[155,175]),
[iquote('0:Res:155.0,175.1')] ).
cnf(408,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[214,175]),
[iquote('0:Res:214.0,175.1')] ).
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(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)],[176,152]),
[iquote('0:SpR:176.0,152.0')] ).
cnf(435,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(u,v))),
inference(spr,[status(thm),theory(equality)],[176,153]),
[iquote('0:SpR:176.0,153.0')] ).
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(2094,plain,
is_a_theorem(implies__dfg(necessarily(skc95),necessarily(skc94))),
inference(sor,[status(thm)],[409,304]),
[iquote('0:SoR:409.0,304.0')] ).
cnf(2099,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(2113,plain,
is_a_theorem(implies__dfg(necessarily(u),strict_implies(v,u))),
inference(rew,[status(thm),theory(equality)],[159,2099]),
[iquote('0:Rew:159.0,2099.0')] ).
cnf(2138,plain,
( ~ is_a_theorem(necessarily(skc95))
| is_a_theorem(necessarily(skc94)) ),
inference(res,[status(thm),theory(equality)],[2094,175]),
[iquote('0:Res:2094.0,175.1')] ).
cnf(2139,plain,
is_a_theorem(necessarily(skc94)),
inference(ssi,[status(thm)],[2138,148,31]),
[iquote('0:SSi:2138.0,148.0,31.1')] ).
cnf(2147,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[2113,175]),
[iquote('0:Res:2113.0,175.1')] ).
cnf(2197,plain,
is_a_theorem(strict_implies(u,skc94)),
inference(sor,[status(thm)],[2147,2139]),
[iquote('0:SoR:2147.0,2139.0')] ).
cnf(2205,plain,
is_a_theorem(implies__dfg(u,skc94)),
inference(sor,[status(thm)],[408,2197]),
[iquote('0:SoR:408.0,2197.0')] ).
cnf(2226,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[419,155]),
[iquote('0:SoR:419.0,155.0')] ).
cnf(2273,plain,
is_a_theorem(strict_implies(u,u)),
inference(sor,[status(thm)],[215,2226]),
[iquote('0:SoR:215.0,2226.0')] ).
cnf(4450,plain,
is_a_theorem(implies__dfg(implies__dfg(necessarily(possibly(u)),possibly(u)),equiv__dfg(possibly(u),necessarily(possibly(u))))),
inference(sor,[status(thm)],[568,158]),
[iquote('0:SoR:568.0,158.0')] ).
cnf(4452,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(u,skc94))),
inference(sor,[status(thm)],[568,2205]),
[iquote('0:SoR:568.0,2205.0')] ).
cnf(4529,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[4452,175]),
[iquote('0:Res:4452.0,175.1')] ).
cnf(4627,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(v,u))),
inference(sor,[status(thm)],[579,2205]),
[iquote('0:SoR:579.0,2205.0')] ).
cnf(4649,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[419,4627]),
[iquote('0:SoR:419.0,4627.0')] ).
cnf(4655,plain,
is_a_theorem(strict_implies(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[215,4649]),
[iquote('0:SoR:215.0,4649.0')] ).
cnf(4656,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[4649,175]),
[iquote('0:Res:4649.0,175.1')] ).
cnf(4658,plain,
is_a_theorem(implies__dfg(necessarily(implies__dfg(skc94,u)),necessarily(u))),
inference(sor,[status(thm)],[409,4655]),
[iquote('0:SoR:409.0,4655.0')] ).
cnf(4661,plain,
is_a_theorem(implies__dfg(strict_implies(skc94,u),necessarily(u))),
inference(rew,[status(thm),theory(equality)],[159,4658]),
[iquote('0:Rew:159.0,4658.0')] ).
cnf(4677,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[4656,162]),
[iquote('0:SoR:4656.0,162.0')] ).
cnf(4994,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,u))),
inference(sor,[status(thm)],[215,4677]),
[iquote('0:SoR:215.0,4677.0')] ).
cnf(5402,plain,
( ~ is_a_theorem(strict_implies(skc94,u))
| is_a_theorem(necessarily(u)) ),
inference(res,[status(thm),theory(equality)],[4661,175]),
[iquote('0:Res:4661.0,175.1')] ).
cnf(5816,plain,
is_a_theorem(necessarily(and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[5402,4994]),
[iquote('0:SoR:5402.0,4994.0')] ).
cnf(5835,plain,
is_a_theorem(strict_implies(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[2147,5816]),
[iquote('0:SoR:2147.0,5816.0')] ).
cnf(5867,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[408,5835]),
[iquote('0:SoR:408.0,5835.0')] ).
cnf(8022,plain,
is_a_theorem(equiv__dfg(and__dfg(skc94,skc94),skc94)),
inference(sor,[status(thm)],[4529,5867]),
[iquote('0:SoR:4529.0,5867.0')] ).
cnf(8039,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,skc94),skc94)),
inference(sor,[status(thm)],[4529,155]),
[iquote('0:SoR:4529.0,155.0')] ).
cnf(8043,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(sor,[status(thm)],[4529,397]),
[iquote('0:SoR:4529.0,397.1')] ).
cnf(8309,plain,
equal(and__dfg(skc94,skc94),skc94),
inference(res,[status(thm),theory(equality)],[8022,163]),
[iquote('0:Res:8022.0,163.0')] ).
cnf(8413,plain,
equal(implies__dfg(u,skc94),skc94),
inference(res,[status(thm),theory(equality)],[8039,163]),
[iquote('0:Res:8039.0,163.0')] ).
cnf(8722,plain,
equal(and__dfg(skc94,implies__dfg(skc94,u)),equiv__dfg(u,skc94)),
inference(spr,[status(thm),theory(equality)],[8413,179]),
[iquote('0:SpR:8413.0,179.0')] ).
cnf(10653,plain,
( ~ is_a_theorem(u)
| equal(u,skc94) ),
inference(res,[status(thm),theory(equality)],[8043,163]),
[iquote('0:Res:8043.1,163.0')] ).
cnf(10778,plain,
equal(strict_implies(implies__dfg(skc94,u),u),skc94),
inference(ems,[status(thm)],[10653,4655]),
[iquote('0:EmS:10653.0,4655.0')] ).
cnf(10779,plain,
equal(strict_implies(u,u),skc94),
inference(ems,[status(thm)],[10653,2273]),
[iquote('0:EmS:10653.0,2273.0')] ).
cnf(10786,plain,
equal(strict_implies(and__dfg(u,v),v),skc94),
inference(ems,[status(thm)],[10653,302]),
[iquote('0:EmS:10653.0,302.0')] ).
cnf(10794,plain,
equal(strict_implies(u,and__dfg(skc94,u)),skc94),
inference(ems,[status(thm)],[10653,4994]),
[iquote('0:EmS:10653.0,4994.0')] ).
cnf(10799,plain,
equal(strict_implies(u,implies__dfg(v,u)),skc94),
inference(ems,[status(thm)],[10653,298]),
[iquote('0:EmS:10653.0,298.0')] ).
cnf(10933,plain,
equal(implies__dfg(necessarily(u),u),skc94),
inference(ems,[status(thm)],[10653,147]),
[iquote('0:EmS:10653.0,147.0')] ).
cnf(11014,plain,
is_a_theorem(implies__dfg(skc94,equiv__dfg(possibly(u),necessarily(possibly(u))))),
inference(rew,[status(thm),theory(equality)],[10933,4450]),
[iquote('0:Rew:10933.0,4450.0')] ).
cnf(12408,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)],[10778,176]),
[iquote('0:SpR:10778.0,176.0')] ).
cnf(12416,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[10799,12408]),
[iquote('0:Rew:10799.0,12408.0')] ).
cnf(12417,plain,
equal(strict_equiv(implies__dfg(skc94,u),u),skc94),
inference(rew,[status(thm),theory(equality)],[8309,12416]),
[iquote('0:Rew:8309.0,12416.0')] ).
cnf(12421,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)],[10794,176]),
[iquote('0:SpR:10794.0,176.0')] ).
cnf(12428,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[10786,12421]),
[iquote('0:Rew:10786.0,12421.0')] ).
cnf(12429,plain,
equal(strict_equiv(u,and__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[8309,12428]),
[iquote('0:Rew:8309.0,12428.0')] ).
cnf(12545,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[12417,191]),
[iquote('1:SpL:12417.0,191.0')] ).
cnf(12546,plain,
equal(implies__dfg(skc94,u),u),
inference(mrr,[status(thm)],[12545,413]),
[iquote('1:MRR:12545.0,413.0')] ).
cnf(12578,plain,
is_a_theorem(equiv__dfg(possibly(u),necessarily(possibly(u)))),
inference(rew,[status(thm),theory(equality)],[12546,11014]),
[iquote('1:Rew:12546.0,11014.0')] ).
cnf(12637,plain,
equal(and__dfg(skc94,u),equiv__dfg(u,skc94)),
inference(rew,[status(thm),theory(equality)],[12546,8722]),
[iquote('1:Rew:12546.0,8722.0')] ).
cnf(12744,plain,
equal(strict_equiv(u,equiv__dfg(u,skc94)),skc94),
inference(rew,[status(thm),theory(equality)],[12637,12429]),
[iquote('1:Rew:12637.0,12429.0')] ).
cnf(13186,plain,
equal(necessarily(possibly(u)),possibly(u)),
inference(res,[status(thm),theory(equality)],[12578,163]),
[iquote('1:Res:12578.0,163.0')] ).
cnf(13189,plain,
equal(possibly(necessarily(not__dfg(u))),not__dfg(possibly(u))),
inference(rew,[status(thm),theory(equality)],[13186,192]),
[iquote('1:Rew:13186.0,192.0')] ).
cnf(14084,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),implies__dfg(skc94,u)),
inference(spr,[status(thm),theory(equality)],[12637,164]),
[iquote('1:SpR:12637.0,164.0')] ).
cnf(14095,plain,
equal(not__dfg(equiv__dfg(not__dfg(u),skc94)),u),
inference(rew,[status(thm),theory(equality)],[12546,14084]),
[iquote('1:Rew:12546.0,14084.0')] ).
cnf(14128,plain,
equal(not__dfg(possibly(necessarily(not__dfg(u)))),possibly(necessarily(possibly(u)))),
inference(spr,[status(thm),theory(equality)],[156,13189]),
[iquote('1:SpR:156.0,13189.0')] ).
cnf(14153,plain,
equal(not__dfg(not__dfg(possibly(u))),possibly(possibly(u))),
inference(rew,[status(thm),theory(equality)],[13189,14128,13186]),
[iquote('1:Rew:13189.0,14128.0,13186.0,14128.0')] ).
cnf(14307,plain,
( ~ is_a_theorem(skc94)
| equal(equiv__dfg(u,skc94),u) ),
inference(spl,[status(thm),theory(equality)],[12744,191]),
[iquote('1:SpL:12744.0,191.0')] ).
cnf(14308,plain,
equal(equiv__dfg(u,skc94),u),
inference(mrr,[status(thm)],[14307,413]),
[iquote('1:MRR:14307.0,413.0')] ).
cnf(14356,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[14308,14095]),
[iquote('1:Rew:14308.0,14095.0')] ).
cnf(14419,plain,
equal(possibly(possibly(u)),possibly(u)),
inference(rew,[status(thm),theory(equality)],[14356,14153]),
[iquote('1:Rew:14356.0,14153.0')] ).
cnf(14708,plain,
~ is_a_theorem(strict_implies(possibly(skc186),possibly(skc186))),
inference(rew,[status(thm),theory(equality)],[14419,157]),
[iquote('1:Rew:14419.0,157.0')] ).
cnf(15223,plain,
~ is_a_theorem(skc94),
inference(rew,[status(thm),theory(equality)],[10779,14708]),
[iquote('1:Rew:10779.0,14708.0')] ).
cnf(15224,plain,
$false,
inference(mrr,[status(thm)],[15223,413]),
[iquote('1:MRR:15223.0,413.0')] ).
cnf(17399,plain,
~ substitution_strict_equiv,
inference(spt,[spt(split,[position(sa)])],[15224,190]),
[iquote('1:Spt:15224.0,43.0,190.0')] ).
cnf(17400,plain,
is_a_theorem(strict_equiv(skc155,skc154)),
inference(spt,[spt(split,[position(s2)])],[43]),
[iquote('1:Spt:15224.0,43.1')] ).
cnf(17403,plain,
~ equal(skc155,skc154),
inference(mrr,[status(thm)],[44,17399]),
[iquote('1:MRR:44.1,17399.0')] ).
cnf(17410,plain,
is_a_theorem(strict_implies(skc155,skc154)),
inference(sor,[status(thm)],[562,17400]),
[iquote('1:SoR:562.0,17400.0')] ).
cnf(17411,plain,
is_a_theorem(strict_implies(skc154,skc155)),
inference(sor,[status(thm)],[534,17400]),
[iquote('1:SoR:534.0,17400.0')] ).
cnf(17420,plain,
is_a_theorem(implies__dfg(skc155,skc154)),
inference(sor,[status(thm)],[408,17410]),
[iquote('1:SoR:408.0,17410.0')] ).
cnf(17442,plain,
is_a_theorem(implies__dfg(skc154,skc155)),
inference(sor,[status(thm)],[408,17411]),
[iquote('1:SoR:408.0,17411.0')] ).
cnf(17444,plain,
equal(implies__dfg(skc155,skc154),skc94),
inference(ems,[status(thm)],[10653,17420]),
[iquote('1:EmS:10653.0,17420.0')] ).
cnf(17451,plain,
equal(implies__dfg(skc154,skc155),skc94),
inference(ems,[status(thm)],[10653,17442]),
[iquote('1:EmS:10653.0,17442.0')] ).
cnf(17474,plain,
equal(and__dfg(implies__dfg(skc154,skc155),skc94),equiv__dfg(skc154,skc155)),
inference(spr,[status(thm),theory(equality)],[17444,179]),
[iquote('1:SpR:17444.0,179.0')] ).
cnf(17480,plain,
equal(and__dfg(skc94,skc94),equiv__dfg(skc154,skc155)),
inference(rew,[status(thm),theory(equality)],[17451,17474]),
[iquote('1:Rew:17451.0,17474.0')] ).
cnf(17481,plain,
equal(equiv__dfg(skc154,skc155),skc94),
inference(rew,[status(thm),theory(equality)],[8309,17480]),
[iquote('1:Rew:8309.0,17480.0')] ).
cnf(17499,plain,
( ~ is_a_theorem(skc94)
| equal(skc155,skc154) ),
inference(spl,[status(thm),theory(equality)],[17481,163]),
[iquote('1:SpL:17481.0,163.0')] ).
cnf(17500,plain,
$false,
inference(mrr,[status(thm)],[17499,413,17403]),
[iquote('1:MRR:17499.0,17499.1,413.0,17403.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : LCL535+1 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jul 4 13:22:36 EDT 2022
% 0.14/0.36 % CPUTime :
% 6.70/6.92
% 6.70/6.92 SPASS V 3.9
% 6.70/6.92 SPASS beiseite: Proof found.
% 6.70/6.92 % SZS status Theorem
% 6.70/6.92 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.70/6.92 SPASS derived 11960 clauses, backtracked 2191 clauses, performed 3 splits and kept 8542 clauses.
% 6.70/6.92 SPASS allocated 119449 KBytes.
% 6.70/6.92 SPASS spent 0:00:06.54 on the problem.
% 6.70/6.92 0:00:00.04 for the input.
% 6.70/6.92 0:00:00.06 for the FLOTTER CNF translation.
% 6.70/6.92 0:00:00.12 for inferences.
% 6.70/6.92 0:00:00.17 for the backtracking.
% 6.70/6.92 0:00:06.06 for the reduction.
% 6.70/6.92
% 6.70/6.92
% 6.70/6.92 Here is a proof with depth 16, length 160 :
% 6.70/6.92 % SZS output start Refutation
% See solution above
% 7.39/7.62 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 km5_op_possibly km5_necessitation km5_axiom_K km5_axiom_M km5_axiom_5 s1_0_m6s3m9b_axiom_m9 modus_ponens axiom_M and_3 substitution_strict_equiv implies_1 and_1 and_2 necessitation axiom_5 axiom_m9 op_possibly op_strict_implies op_implies_and implies_2 op_equiv axiom_K op_strict_equiv implies_3 equivalence_3
% 7.39/7.62
%------------------------------------------------------------------------------